Official logos or icons for R, RStudio and Jamovi.

1 Preface

Welcome to “Exploring Ecological Data with R and Jamovi: A Beginner’s Guide to Statistical Data Analysis.” This manual is designed to be your comprehensive companion on the journey to becoming proficient in ecological data analysis using two powerful tools: R and Jamovi.

In the realm of ecology, data analysis is at the heart of understanding the intricate relationships within ecosystems, quantifying environmental impacts, and making informed decisions for conservation and research. The dynamic duo of R and Jamovi empowers ecologists and researchers to unlock the potential hidden within ecological datasets.

This manual is born out of the belief that mastering these tools should be an accessible and engaging experience for all, whether you are a seasoned ecologist looking to expand your analytical toolkit or a newcomer eager to embark on your ecological research journey.

What You Will Discover:

  • Installation and Setup: In Chapter 1, we provide step-by-step guidance on installing R, RStudio, and Jamovi on your preferred operating system. Get ready to embark on a data analysis adventure!

  • Data Import and Cleaning: Chapter 2 introduces you to the critical process of importing ecological datasets into R and Jamovi. Learn techniques for cleaning and preprocessing data, ensuring your analyses are based on high-quality, error-free data.

  • Exploratory Data Analysis (EDA): Dive into Chapter 3, where you’ll discover the fascinating world of Exploratory Data Analysis (EDA). Visualize and summarize ecological data, uncover patterns, relationships, and outliers that hide within your datasets.

  • Statistical Tests: Chapter 4 demystifies statistical hypothesis testing, a fundamental aspect of ecological research. Explore common tests used in ecology, from t-tests to ANOVA and non-parametric tests, and learn how to perform them in R and Jamovi.

  • Regression Analysis: In Chapter 5, you’ll delve into regression analysis, a powerful tool for modeling ecological relationships. Understand linear and logistic regression and gain the skills to interpret regression outputs.

  • Data Visualization: Chapter 6 unveils the art of data visualization. Learn to create informative graphs and plots that effectively communicate your ecological findings.

  • Advanced Topics: As you progress, Chapter 7 opens doors to more advanced topics like multivariate analysis, spatial analysis, and time series analysis, expanding your ecological research possibilities.

  • Case Studies: Throughout this guide, you’ll encounter real-world ecological case studies in Chapter 8. These practical examples demonstrate how R and Jamovi are applied to solve ecological problems, offering valuable insights into the application of these tools in ecological research.

Your Ecological Journey Begins:

With this manual as your guide, you’re embarking on a journey of discovery, analysis, and ecological understanding. We encourage you to embrace every chapter, practice with real datasets, and apply what you learn to your own ecological questions.

We extend our gratitude to all those who have contributed to this manual, and we’re excited to accompany you on your ecological data analysis adventure. Your passion for ecology and your drive to make data-driven decisions are the driving forces behind this endeavor.

Now, let’s dive into the fascinating world of ecological data analysis with R and Jamovi. Your ecological journey begins here.

Happy analyzing!

………………………………

Dr. Jimmy Moses (Ph.D.)

Department of Forestry,

The Papua New Guinea University of Technology

2 Introduction

Ecology, the study of the interactions between organisms and their environment, generates vast amounts of data. Analyzing this data is crucial for understanding ecosystems, making informed conservation decisions, and addressing environmental challenges. Statistical data analysis is the cornerstone of ecological research, enabling scientists to derive meaningful insights from complex ecological datasets.

This guide, “Exploring Ecological Data with R and Jamovi,” is tailored for beginners in the field of ecology who are eager to harness the power of statistical analysis to unravel ecological mysteries. Whether you’re a budding ecologist, a conservation enthusiast, or a student embarking on ecological research, this guide will serve as your compass through the intricate world of data analysis.

Why R and Jamovi?

R is a popular open-source statistical programming language renowned for its versatility and power in data analysis. It has become the lingua franca of data science and is extensively used in ecological research. R provides a vast ecosystem of packages tailored to various ecological analyses, making it an invaluable tool for ecologists.

Jamovi, on the other hand, is a user-friendly statistical software designed with accessibility in mind. Its intuitive graphical interface and point-and-click functionality make it an excellent choice for beginners. Jamovi seamlessly integrates with R, allowing users to transition from a simple point-and-click environment to more complex analyses in R as they gain proficiency.

Who Is This Guide For?

This guide is tailored for:

  • Students and researchers entering the field of ecology.

  • Conservationists and environmentalists interested in data-driven decision-making.

  • Anyone curious about using R and Jamovi for data analysis, whether in ecology or any other field.

Embark on your ecological data analysis journey with confidence. This guide aims to demystify statistical analysis using R and Jamovi, providing you with the skills and knowledge to explore ecological data, ask critical questions, and contribute to the understanding and conservation of our natural world. Let’s begin our exploration of ecological data with R and Jamovi.

2.1 Purpose of this Manual

This comprehensive manual is intended to serve as a detailed and user-friendly guide to the installation and competent use of core data analysis tools: R, RStudio, and Jamovi. These software programmes play critical roles in a variety of sectors, including forestry and ecology, where they are essential for conducting demanding statistical analysis, creating intelligent data visualisations, and driving significant research initiatives.

Notably, this training manual played an important role as an integral component of a workshop held at the Department of Forestry, Papua New Guinea University of Technology. The primary goal of this course was to empower its participants, the majority of whom were novices, by providing them with the required tools and competences for competent data analysis within the specialised environment.

This manual, which will be converted to a handbook in the near future, will be regularly expanded to cover complex data analysis techniques such as geographical mapping and modelling. These planned upgrades will serve as the foundation for a complete manual that will take your data analysis skills to the next level. These changes are intended to address the growing expectations of forestry and ecological researchers, professionals, and students.

Furthermore, this manual will serve as a foundation for future workshops. These workshops aim to dive further into complicated data analysis, sophisticated modelling methodologies, and the use of geospatial data for improved ecological insights. We are devoted to equipping participants with cutting-edge information and practical skills that will enable them to flourish in the dynamic fields of forestry and ecology.

Through these future developments and workshops, we aim to foster a community of proficient data analysts and researchers who can make significant contributions to the sustainable management of our natural ecosystems.

Key Outcomes:

  • Tool Proficiency: Participants are equipped with the proficiency to harness the capabilities of R, RStudio, and Jamovi as powerful aids in their data analysis workflows.

  • Statistical Analysis: Participants will obtain the knowledge and practical skills required for in-depth statistical analysis, allowing them to test hypotheses, investigate relationships, and develop data-driven conclusions.

  • Data Visualization: The handbook instructs users on how to use these tools to generate useful and aesthetically appealing data visualizations, which are an important feature of data communication.

  • Research Empowerment: With these essential tools and the know-how to properly use them, participants are better positioned to contribute meaningfully to research efforts, particularly in forestry and ecology.

Readers will not only obtain the skills to set up and utilize the aforementioned programs by immersing themselves in the contents of this handbook, but they will also receive vital insights into their practical applications. This newly acquired skill will not only improve their capacity to perform reliable data analysis but will also enable them to make significant contributions to the domains of forestry and ecology or any other related fields.

3 Chapter 1: Installation and Setup

3.1 Prerequisites

Before you begin the installation process, it is essential to ensure that you meet the following prerequisites:

  • Internet Connection: You must have a stable and active internet connection to download the required software packages and updates.

  • Administrator Privileges (Windows): If you are using a Windows operating system, you may need administrator privileges to install software. Ensure that you have the necessary permissions.

  • Operating System Compatibility: Verify that your operating system is compatible with the software you intend to install. Each software package has specific system requirements, which will be outlined in the installation sections.

  • Basic Computer Skills: This manual assumes that you have basic computer skills, including the ability to navigate your operating system and use a web browser.

  • Storage Space: Ensure that you have sufficient disk space available to accommodate the software installations. The installation sections will specify the approximate storage requirements.

  • Hardware Requirements: Check if your computer meets the hardware requirements specified by the software developers. This information is usually available on the respective software websites.

Computers operate on three of the most common operating systems: Windows, Mac OS, and Linux. Depending on your operating system, follow the installation instructions relevant to your specific platform. The process will differ slightly for Windows, macOS, and Linux users, so ensure you select the appropriate set of instructions based on your system.

3.2 Installing R

3.2.1 Windows

3.2.1.1 Downloading R:

  1. Open your web browser and navigate to the R download page (download here).

  2. Click on the “Download R for Windows” link.

  3. Choose a CRAN mirror (usually the one geographically closest to you) and click on its link.

  4. Download the base version of R for Windows by clicking on the “install R for the first time” link.

3.2.1.2 Installing R:

  1. Locate the downloaded R installer (an .exe file) and double-click it.

  2. Follow the installation wizard’s instructions:

    • Choose the language.

    • Accept the terms of the license.

    • Select the components you want to install (usually, you can leave the default settings).

    • Choose the installation location (you can leave the default).

    • Click “Next” to start the installation.

Once the installation is complete, you can now run R by searching for “R” in the Windows Start menu.

3.2.1.3 Downloading and Installing RTools in Windows:

RTools is a collection of tools required for building and installing R packages from source on Windows. It is essential for users who want to compile and install R packages from CRAN or other sources. Here are the steps to download and install RTools on a Windows system:

  1. Download RTools:

    • Open your web browser and navigate to the RTools download page (download here).

    • On the RTools download page, scroll down to find the “Download Rtools” section.

    • Click on the link that corresponds to the version of RTools recommended for your version of R. It is essential to match the RTools version with the R version you have installed. For example, if you have R version 4.1.x, download the RTools version recommended for R 4.1.x.

    • You will be directed to a new page with a list of download links. Click on the link that says “install.exe” to download the RTools installer.

  2. Installing RTools:

    • Locate the downloaded RTools installer (an .exe file) and double-click it to start the installation.

    • Follow the installation wizard’s instructions:

      • Choose the language.

      • Accept the terms of the license.

      • Select the components you want to install. It is recommended to install all components, so leave the default settings selected.

      • Choose the installation location. By default, RTools will install in the “C:\Rtools” directory. You can change this location if necessary.

      • Click “Next” to start the installation.

    • During the installation, you may see a message about modifying the system PATH. Make sure to select the option that adds RTools to the system PATH. This is essential for R to find and use RTools when building packages.

    • Once the installation is complete, you can click “Finish” to exit the installer.

  3. Verifying the Installation:

    • To verify that RTools has been installed correctly, open R or RStudio.

  4. In the R console, you can run the following command to check if RTools is found:

    Sys.which("make")

  5. If the installation was successful, you should see a path to the make.exe executable associated with RTools.

That’s it! You have successfully downloaded and installed RTools on your Windows system. You are now ready to build and install R packages from source when needed.

3.2.2 macOS

3.2.2.1 Downloading R:

  1. Open your web browser and navigate to the R download page (download here). Note: the use of X11 (including tcltk) requires XQuartz (version 2.8.5 or later). Always re-install XQuartz when upgrading your macOS to a new major version.

  2. Click on the “Download R for (Mac) OS X” link.

  3. Download the latest R framework (pkg file) by clicking on the link.

3.2.2.2 Installing R:

  1. Locate the downloaded R framework (a .pkg file) and double-click it.

  2. Follow the installation instructions in the installer:

    • Agree to the license terms.

    • Choose the installation location (you can leave the default).

    • Click “Install” to start the installation.

  3. Once the installation is complete, you can run R by searching for “R” in the Applications folder.

3.2.3 Linux (Ubuntu)

3.2.3.1 Downloading R:

  1. Open a terminal window.

  2. Enter the following commands one by one to add the CRAN repository and the key:

    sudo apt update
sudo apt install r-base

3.2.3.2 Installing R:

  1. Once the installation is complete, you can run R by opening the terminal and typing R.

3.3 Installing RStudio

3.3.1 Windows

3.3.1.1 Downloading RStudio:

  1. Open your web browser and navigate to the RStudio download page (download here).

  2. Scroll down to the “RStudio Desktop” section.

  3. Click on the “Download” button under the “RStudio Desktop (Free)” option.

  4. Download the RStudio installer for Windows.

3.3.1.2 Installing RStudio:

  1. Locate the downloaded RStudio installer (an .exe file) and double-click it.

  2. Follow the installation wizard’s instructions:

    • Choose the language.

    • Accept the license agreement.

    • Choose the installation location (you can leave the default).

    • Select additional tasks (optional).

    • Click “Install” to begin the installation.

  3. Once the installation is complete, you can run RStudio by searching for “RStudio” in the Windows Start menu.

3.3.2 macOS

3.3.2.1 Downloading RStudio:

  1. Open your web browser and navigate to the RStudio download page (download here).

  2. Scroll down to the “RStudio Desktop” section.

  3. Click on the “Download” button under the “RStudio Desktop (Free)” option.

  4. Download the RStudio installer for macOS.

3.3.2.2 Installing RStudio:

  1. Locate the downloaded RStudio installer (a .dmg file) and double-click it.

  2. A new window will open. Drag the RStudio icon into the Applications folder.

  3. Once the copy is complete, you can run RStudio from your Applications folder.

3.3.3 Linux (Ubuntu)

3.3.3.1 Downloading RStudio:

  1. Open a terminal window.

  2. Enter the following command to download the RStudio package (download here):

    sudo apt-get install gdebi-core
wget https://download1.rstudio.org/desktop/bionic/amd64/rstudio-1.4.1717-amd64.deb

3.3.3.2 Installing RStudio:

  1. After the download is complete, use the following command to install RStudio:

    sudo gdebi rstudio-1.4.1717-amd64.deb

  2. Once the installation is complete, you can run RStudio by searching for “RStudio” in the applications menu.

3.4 Installing Jamovi

3.4.1 Windows

3.4.1.1 Downloading Jamovi:

  1. Open your web browser and navigate to the Jamovi download page (download here).

  2. Click on the “Download for Windows” button.

  3. Download the Jamovi installer for Windows.

3.4.1.2 Installing Jamovi:

  1. Locate the downloaded Jamovi installer (an .exe file) and double-click it.

  2. Follow the installation wizard’s instructions:

    • Choose the installation location (you can leave the default).

    • Select additional tasks (optional).

    • Click “Install” to begin the installation.

  3. Once the installation is complete, you can run Jamovi by searching for “Jamovi” in the Windows Start menu.

3.4.2 macOS

3.4.2.1 Downloading Jamovi:

  1. Open your web browser and navigate to the Jamovi download page (download here).

  2. Click on the “Download for macOS” button.

  3. Download the Jamovi installer for macOS.

3.4.2.2 Installing Jamovi:

  1. Locate the downloaded Jamovi installer (a .dmg file) and double-click it.

  2. A new window will open. Drag the Jamovi icon into the Applications folder.

  3. Once the copy is complete, you can run Jamovi from your Applications folder.

3.4.3 Linux (Ubuntu)

3.4.3.1 Downloading Jamovi:

  1. Open a terminal window.

  2. Enter the following commands to download and install Jamovi (install via this page):

    sudo add-apt-repository ppa:jamovi/jamovi
sudo apt-get update
sudo apt-get install jamovi

# or install via flatpak
flatpak install flathub org.jamovi.jamovi
flatpak run org.jamovi.jamovi

3.4.3.2 Installing Jamovi:

  1. Once the installation is complete, you can run Jamovi by searching for “Jamovi” in the applications menu.

3.5 Verifying Installations

3.5.1 Checking R Installation

  • Windows:

    1. Open R by searching for “R” in the Start menu.

    2. The R console should appear. You can start using R by entering commands.

  • macOS:

    1. Open the Applications folder and run R.

    2. The R console should open, allowing you to use R.

  • Linux (Ubuntu):

    1. Open a terminal and type R.

    2. The R console should open.

3.5.2 Checking RStudio Installation

  • Windows:

    1. Open RStudio by searching for “RStudio” in the Start menu.

    2. The RStudio IDE should open, ready for use.

  • macOS:

    1. Open the Applications folder and run RStudio.

    2. The RStudio IDE should open.

  • Linux (Ubuntu):

    1. Open the applications menu and search for “RStudio.”

    2. Launch RStudio from the menu.

3.5.3 Checking Jamovi Installation

  • Windows:

    1. Open Jamovi by searching for “Jamovi” in the Start menu.

    2. The Jamovi interface should open.

  • macOS:

    1. Open the Applications folder and run Jamovi.

    2. The Jamovi interface should open.

  • Linux (Ubuntu):

    1. Open the applications menu and search for “Jamovi.”

    2. Launch Jamovi from the menu.

3.6 Updating and Maintaining Software

3.6.1 Updating R

  • Regularly update R to ensure you have the latest features and bug fixes.

  • Windows and macOS users can download the latest R installer and reinstall R. Your packages and scripts will remain intact.

  • Linux users can use package managers like apt to update R:

    sudo apt-get update
sudo apt-get upgrade r-base

3.6.2 Updating RStudio

  • For RStudio updates, download the latest version from the RStudio website and reinstall it. Your projects and settings will be preserved.

3.6.3 Updating Jamovi

  • Jamovi typically updates itself automatically when you launch the software. Ensure you have an internet connection for updates to occur.

3.7 Troubleshooting

3.7.1 Common Installation Issues

3.7.1.1 Difficulty in Downloading Software

  • If you encounter difficulties downloading R, RStudio, or Jamovi, ensure you have a stable internet connection.

  • Try using an alternative download mirror if the default one is slow or unresponsive.

  • Disable any firewall or security software temporarily, as they may block downloads.

3.7.1.2 Compatibility Issues

  • Ensure that you are downloading the correct version of the software that matches your operating system (Windows, macOS, Linux) and architecture (32-bit or 64-bit).

  • Verify that your operating system meets the minimum requirements for the software.

3.7.1.3 Missing Dependencies

  • On Linux, if you encounter missing dependencies when installing R, RStudio, or Jamovi, you can usually install them using your system’s package manager (e.g., apt for Ubuntu).

3.7.2 Package Installation Issues

3.7.2.1 R Package Installation

  • If you encounter issues when installing R packages using the install.packages() function, ensure you have an internet connection.

  • Some packages may require additional system libraries. Check the package documentation for any specific requirements.

  • If you receive errors related to permissions, consider running R or RStudio with administrative privileges (e.g., “Run as administrator” on Windows).

3.7.2.2 Jamovi Module Installation

  • When installing Jamovi modules (extensions), ensure that you are using a compatible version of Jamovi.

  • If a module installation fails, check if there are any error messages provided. These messages often indicate the cause of the issue.

3.7.2.3 Resources for Assistance

  • If you encounter installation or package-related issues that are not covered here, consider seeking help from the following resources:

    • Online Forums: Visit community forums or discussion boards related to R, RStudio, and Jamovi. Experienced users often provide solutions to common problems.

    • Official Documentation: Consult the official documentation for each software. They often include troubleshooting sections.

    • User Communities: Join user communities or mailing lists where you can ask questions and seek assistance from experienced users.

3.8 Cloud Registration

RStudio Cloud is a powerful cloud-based platform that allows you to access the RStudio Integrated Development Environment (IDE) from anywhere with an internet connection and a web browser. This means you can work on your data analysis projects without being tied to a specific computer or location.

3.8.1 Advantages of Using RStudio Cloud and Cloud Computing:

  1. Accessibility: With RStudio Cloud, you can access your projects and data from virtually anywhere, whether you’re at home, in the office, or on the go. All you need is an internet connection and a web browser.

  2. Collaboration: RStudio Cloud makes collaboration easy. You can share your projects with colleagues or collaborators, allowing them to work on the same analysis, view your code, and provide input in real-time, regardless of their physical location.

  3. Version Control: RStudio Cloud often integrates with version control systems like Git and GitHub. This enables you to track changes in your projects, collaborate with others, and maintain a history of your work.

  4. Resource Scalability: Cloud computing provides the flexibility to scale your computing resources as needed. If you require more processing power or memory for a specific analysis, you can often adjust your cloud resources accordingly.

  5. Cost Efficiency: Many cloud platforms offer a pay-as-you-go pricing model, which can be cost-effective, especially for users who don’t require constant high-performance computing. You only pay for the resources you use.

  6. Security: Reputable cloud providers invest heavily in security measures to protect your data. They often offer encryption, secure access controls, and data redundancy to safeguard your work.

  7. Automatic Backups: Cloud platforms typically provide automated backup solutions, reducing the risk of data loss due to hardware failures or other issues.

  8. Device Independence: Since RStudio Cloud runs in a web browser, it’s compatible with various devices, including laptops, desktops, tablets, and even smartphones, making it highly versatile.

  9. Reduced Setup Time: Setting up and configuring R, RStudio, and packages can be time-consuming on a local machine. RStudio Cloud simplifies this process, allowing you to focus on your analysis rather than software installation and maintenance.

  10. Learning Opportunities: For educators and trainers, RStudio Cloud offers a convenient way to teach R and data analysis. Students can access a consistent, pre-configured environment, eliminating the need for individual software installations.

In summary, RStudio Cloud and cloud computing provide numerous advantages, including enhanced accessibility, collaboration, cost efficiency, security, and scalability. These benefits make cloud-based platforms like RStudio Cloud valuable tools for data analysts, researchers, educators, and anyone who wants the flexibility of working with data and code from anywhere with ease.

3.8.2 Sign Up for a RStudio Cloud Account

  1. Open your web browser and go to the RStudio Cloud website (https://posit.cloud/).

  2. Click the “Sign Up” button to create a new account.

  3. Fill out the required information, including your name, email address, and a password for your RStudio Cloud account.

  4. Read and accept the Terms of Service and Privacy Policy.

  5. Click the “Sign Up” button to complete the registration process.

3.8.3 Confirm Your Email Address

  1. Check your email inbox for a message from RStudio Cloud.

  2. Open the email and click the confirmation link provided. This step verifies your email address and activates your account.

3.8.4 Create a New Project

  1. After confirming your email, log in to your RStudio Cloud account.

  2. Click the “New Project” button on the dashboard.

  3. Give your project a name and, optionally, a description.

  4. Choose a project privacy setting (private or public) based on your preferences.

  5. Click the “Create Project” button.

3.8.5 Access Your RStudio Workspace

  1. Once your project is created, you’ll be taken to your RStudio workspace within your web browser.

  2. Here, you have access to the RStudio IDE, which includes a script editor, console, and other tools for data analysis.

3.8.6 Working with RStudio Cloud

You can now start working with R and RStudio within your RStudio Cloud environment. Here are some key points to remember:

  • You can write R scripts, execute code, and work with datasets just like you would in a local RStudio installation.

  • Your work is saved automatically within your RStudio Cloud project.

  • You can upload and download files, including R scripts and datasets, to and from your project.

  • Collaborate with others by sharing your project or working on shared projects.

  • RStudio Cloud provides a flexible environment that allows you to install additional R packages and extensions as needed.

  • To end your session, simply close your web browser. Your work will be saved, and you can resume from where you left off the next time you log in.

3.8.7 Managing Your Account

You can access your account settings, change your password, and manage your projects by clicking on your profile picture or username in the top right corner of the RStudio Cloud interface.

That’s it! You’ve successfully set up and started using RStudio Cloud, which provides a convenient way to work with R and RStudio from any device with an internet connection and a web browser.

3.9 Testing R Package Installation

3.9.1 Introduction

To ensure that your R environment is fully functional and equipped with essential packages for data analysis, we will test the installation of key R packages. These packages include devtools, remotes, tidyverse, and rstatix. This process will help verify that the packages can be installed and loaded successfully within RStudio.

3.9.2 Installing and Loading Packages

Follow these steps to install and load the required R packages using RStudio:

  1. Open RStudio:

    • Launch RStudio by searching for “RStudio” in your computer’s application menu.

  2. Installing devtools and remotes:

    • In the RStudio console, enter the following commands to install the devtools and remotes packages:

      install.packages("devtools")
install.packages("remotes")

    • Wait for the installations to complete. You may be prompted to select a CRAN mirror; choose a location geographically close to you for faster downloads.

  3. Loading devtools and remotes:

    • After installation, load the devtools and remotes packages by entering these commands in the console:

      library(devtools)
library(remotes)

  4. Installing tidyverse and rstatix:

    • With devtools and remotes loaded, you can now install the tidyverse and rstatix packages, which are essential for data manipulation and statistical analysis:

      install.packages("tidyverse")
remotes::install_github("kassambara/rstatix")

    • Allow the installations to proceed. The remotes package is used to install rstatix directly from its GitHub repository.

  5. Loading tidyverse and rstatix:

    • Once installed, load the tidyverse and rstatix packages with the following commands:

      library(tidyverse)
library(rstatix)

  6. Verifying Package Loading

    • To confirm that the packages have been successfully loaded, you can execute a simple test. For instance, you can try running the following command, which uses a function from the tidyverse package:

      ggplot2::qplot(1:10, rnorm(10))

If the packages have been loaded correctly, you should see a basic scatterplot generated by ggplot2.

Testing the installation and loading of these packages ensures that your R environment is ready for data analysis tasks. By successfully installing and loading devtools, remotes, tidyverse, and rstatix, you have access to a powerful set of tools for data manipulation, visualization, and statistical analysis within RStudio.

You are now well-equipped to embark on data analysis projects with R, and you can confidently explore additional packages tailored to your specific needs.

3.10 Summary of Key Steps

In this manual, we have provided comprehensive guidance on the installation of essential data analysis tools: R, RStudio, and Jamovi. These tools are invaluable for conducting statistical analysis, data visualization, and research in various fields.

To recap the key steps covered in this manual:

  1. Installing R:

    • Choose the appropriate version for your operating system (Windows, macOS, or Linux).

    • Follow the step-by-step instructions provided to download and install R.

    • Verify the successful installation of R by launching the R console.

  2. Installing RStudio:

    • Select the correct version of RStudio for your operating system.

    • Follow the installation instructions to download and install RStudio.

    • Confirm the successful installation of RStudio and its integration with R.

  3. Installing Jamovi:

    • Download Jamovi for your operating system.

    • Execute the installation process as guided in the manual.

    • Validate the installation by launching Jamovi.

  4. Verifying Installations:

    • Ensure that R, RStudio, and Jamovi open without errors.

    • Confirm that you can access the R console and RStudio IDE smoothly.

  5. Updating and Maintaining Software:

    • Regularly check for updates to R, RStudio, and Jamovi to benefit from the latest features and bug fixes.

    • Follow the guidelines provided to update each software component.

  6. Troubleshooting:

    • Consult the troubleshooting section if you encounter common installation or package-related issues.

    • Utilize online forums, official documentation, and user communities to seek assistance for more complex problems.

3.10.1 Next Steps

Now that you have successfully installed R, RStudio, and Jamovi, you are equipped with powerful tools for data analysis, statistical modeling, and research. Your next steps might include:

  • Learning and Practicing: Explore online tutorials and resources to enhance your skills in using R, RStudio, and Jamovi for data analysis.

  • Working on Projects: Apply your newly acquired knowledge to real-world projects, research, or coursework.

  • Exploring Packages: Explore and install additional R packages that cater to your specific analytical needs.

  • Collaborating: Share your work with colleagues or collaborate on data analysis projects using these tools.

  • Staying Informed: Stay updated with the latest developments and updates for R, RStudio, and Jamovi by subscribing to relevant newsletters or communities.

  • Supporting Others: Share your knowledge and help others who are beginning their journey with these tools.

3.10.2 Final Remarks

I hope that this installation manual has been a valuable resource in getting you started with R, RStudio, and Jamovi. These tools offer limitless possibilities for data analysis and research. Remember that practice, exploration, and continuous learning will enhance your proficiency in using these tools effectively. Thank you for choosing this manual as your guide to installing and working with these essential data analysis tools. We wish you success in your data analysis endeavors!

3.11 Introducing R and Jamovi

We will continue our exploration of data analysis tools by introducing you to two powerful platforms: R and Jamovi. As a brief recap of our previous session, you’ve learned about the significance of inferential statistics and its applications in forestry and ecological research (see supplementary section for more detail information). Furthermore, this section provides an introduction to R and Jamovi, covering packages and modules, installation of R and RStudio, basic R commands, data structures, and importing data. It also introduces Jamovi’s interface, data import, and basic data manipulation. Now, we will dive into the practical aspects of using R and Jamovi for data analysis.

3.11.1 R Packages and Modules in Jamovi

R Packages and Jamovi Modules are both essential components of statistical analysis and data manipulation, but they differ in several key ways:

3.11.1.1 R Packages:

  1. Language Foundation: R packages are part of the R programming language. R is a versatile, open-source scripting language and environment explicitly designed for statistical computing and data analysis.

  2. Community-Driven: R packages are developed by a diverse community of statisticians, data scientists, and programmers from around the world. Anyone can contribute to or create R packages, leading to a vast ecosystem with thousands of packages.

  3. Functionality: R packages provide a wide range of functions and tools for statistical analysis, data visualization, machine learning, and more. These packages can be highly specialized, focusing on specific tasks or domains.

  4. Flexibility: R packages offer a high level of customization and flexibility. Users can write their R code, combining functions from various packages to create tailored solutions.

  5. Syntax: R uses its syntax, which is based on function calls and assignments. Users need to learn R’s specific syntax to work with R packages effectively.

  6. Integration: R packages can be integrated with other programming languages like Python and C++, enabling users to harness the capabilities of these languages within R.

  7. Code-Based: Using R packages often requires writing code or scripts to perform data analysis and visualization tasks. It’s suitable for those comfortable with programming.

3.11.1.2 Jamovi Modules:

  1. Graphical User Interface (GUI): Jamovi is a statistical software that provides a point-and-click graphical user interface (GUI). Jamovi modules are components within this GUI that allow users to perform specific analyses without writing code.

  2. Built-In Functionality: Jamovi modules come pre-installed with the software and cover a wide range of statistical analyses. Users can access these modules through a user-friendly interface, eliminating the need for coding.

  3. Ease of Use: Jamovi is designed for users who may not have programming experience. It simplifies statistical analysis by providing intuitive menus, buttons, and options.

  4. Accessibility: Jamovi is an excellent choice for beginners and users who prefer not to write code. It offers a low learning curve and helps users quickly perform common statistical tasks.

  5. Interactivity: Jamovi allows users to interact with their data visually. Users can load datasets, click through options, and see immediate results in the interface.

  6. Modular Design: Jamovi follows a modular design, meaning users can combine different modules to create analysis pipelines. This modular approach promotes reusability and versatility.

  7. Scripting and R Integration: While Jamovi emphasizes point-and-click functionality, it also includes an R Syntax mode. This mode enables users to write and execute R code within Jamovi, combining the strengths of both approaches.

R Packages are code libraries for the R programming language, offering extensive functionality and flexibility but requiring coding skills. Jamovi Modules, on the other hand, are part of a user-friendly statistical software with a GUI, designed for ease of use and accessibility, making statistical analysis more accessible to a broader audience, including those without coding experience.

3.11.2 Getting Started with R

3.11.2.1 Installing R and RStudio

3.11.2.1.1 Installing R:

You can install R by following these steps:

  1. Visit the CRAN (Comprehensive R Archive Network) website for your operating system (Windows, macOS, or Linux): https://cran.r-project.org/mirrors.html

  2. Download the R installer for your OS and follow the installation instructions.

3.11.2.1.2 Installing RStudio:

Once R is installed, you can proceed to install RStudio:

  1. Visit the RStudio download page: https://www.rstudio.com/products/rstudio/download/

  2. Download the appropriate RStudio installer for your OS (RStudio Desktop is recommended for most users).

  3. Install RStudio by following the installation instructions.

3.11.2.2 Understanding R Interface and Basics

3.11.2.2.1 Launch RStudio:

Open RStudio by searching for “RStudio” in your computer’s application menu.

3.11.2.2.2 R Interface:

  • The RStudio interface consists of several panels, including the script editor, console, environment, and plots.

  • The script editor is where you write and execute R code.

  • The console displays R’s output and can be used for direct command entry.

3.11.2.3 Basic Commands and Data Structures:

Let’s explore some basic commands and data structures:

# Basic Arithmetic
2 + 3       # Addition: Calculates and returns 2 plus 3, which is 5.
5 - 2       # Subtraction: Calculates and returns 5 minus 2, which is 3.
4 * 6       # Multiplication: Calculates and returns 4 times 6, which is 24.
8 / 4       # Division: Calculates and returns 8 divided by 4, which is 2.

# Assigning Values to Variables
x <-
  10     # Assign 10 to the variable x: Creates a variable 'x' and assigns the value 10 to it.
y <-
  5      # Assign 5 to the variable y: Creates a variable 'y' and assigns the value 5 to it.

# Vectors
my_vector <-
  c(3, 6, 9, 12)  # Create a numeric vector: Constructs a vector 'my_vector' with the values 3, 6, 9, and 12.
length(my_vector)            # Check the length of the vector: Returns the number of elements in 'my_vector' (4).
mean(my_vector)              # Calculate the mean of the vector: Computes the average of the values in 'my_vector' (7.5).

# Data Frames (a common data structure in R)
# Create a sample forestry dataset: Generates a data frame 'forest_data' with columns 'TreeSpecies', 'Height', and 'Diameter'.
forest_data <- data.frame(
  TreeSpecies = c("Oak", "Pine", "Maple", "Birch"),
  Height = c(25, 20, 18, 22),
  Diameter = c(10, 8, 7, 9)
)

print(forest_data)  # Print the data frame 'forest_data': Displays the content of the data frame.

R Code Explanation:

  • Codes above illustrate basic arithmetic operations, variable assignment, the creation and manipulation of vectors, and the construction of a data frame in R. It demonstrates fundamental operations commonly used in data analysis and manipulation in R.

3.11.2.4 Importing Data into R

R allows you to import data from various file formats, such as CSV, Excel, or databases. Here’s an example of importing a CSV file:

# Check if the "pacman" package is available; if not, install it and load it
if (!require("pacman")) {
  install.packages("pacman")
  require(pacman)
}

# Use the "pacman" package to load multiple packages at once
pacman::p_load(
  rstatix,
  # rstatix: Provides functions for statistical analysis
  tidyverse,
  # tidyverse: A collection of packages for data manipulation and visualization
  easystats,
  # easystats: Provides easy-to-use functions for statistical analysis
  readr,
  # readr: Used for reading data from various file formats
  magrittr,
  # magrittr: Provides a pipe operator (%>%) for easier data manipulation
  knitr,
  # knitr: Used for dynamic report generation
  report,
  # report: A package for creating and formatting reports
  scatr,
  # scatr: Tools for exploratory data analysis and visualization
  jmv,
  # jmv: Tools for statistical analysis and hypothesis testing
  haven,
  # haven: A package for reading and writing data in SAS format
  foreign,
  # foreign: A package for reading and writing data in various formats
  performance,
  # performance: Provides functions for assessing model performance
  ggthemes,
  here,
  install = TRUE,
  # Install packages if not already installed
  update = TRUE   # Update packages if newer versions are available
  
)

# Load the iris dataset
data("iris")          # Load the built-in iris dataset into the R environment

# Uncomment the following line to view the dataset in a separate window
# View(iris)

# Display a concise summary of the iris dataset
tibble::glimpse(iris)

# Create a scatter plot using ggplot2 to visualize the relationship
# between Sepal.Length and Sepal.Width
ggplot(data = iris, aes(x = Sepal.Length, y = Sepal.Width)) +
  geom_point() +                     # Add points to the plot
  geom_smooth(method = "lm")         # Add a linear regression line

# Read the iris dataset from a CSV file into a variable called iris_import
iris_import <-
  read_csv(file = here::here("docs", "data", "Filtered.csv"))

# Uncomment the following line to view the imported dataset
# View(iris_import)

# Export the original iris dataset to a CSV file at the specified file path
utils::write.csv(
  x = iris,
  # Dataset to export (iris)
  file = "./data/iris.csv",
  # File path to save the CSV
  fileEncoding = "UTF-8",
  # Encoding of the CSV file
  row.names = FALSE                    # Exclude row names in the CSV
)

# Use getwd() to show your current working directory path

R Code Explanation:

  • The code first checks if the “pacman” package is available using the require function. If it’s not available, it installs the “pacman” package and then loads it using require.

  • The pacman::p_load function is used to load multiple packages at once. Each package listed is loaded, and if any of them are not installed, they will be installed (install = TRUE). Additionally, if newer versions of packages are available, they will be updated (update = TRUE).

  • Here’s a brief explanation of each package:

    • rstatix: Provides functions for statistical analysis, particularly for tidyverse users.

    • tidyverse: A collection of packages (e.g., dplyr, ggplot2) for data manipulation and visualization.

    • easystats: Provides easy-to-use functions for various statistical analyses.

    • readr: Used for reading data from various file formats (e.g., CSV, Excel).

    • magrittr: Provides the pipe operator (%>%) for easier data manipulation.

    • knitr: Used for dynamic report generation, often in combination with R Markdown.

    • report: A package for creating and formatting reports.

    • scatr: Provides tools for exploratory data analysis and visualization.

    • jmv: Contains tools for statistical analysis and hypothesis testing.

    • performance: Provides functions for assessing model performance.

This code is an efficient way to ensure that all the necessary packages are available and up-to-date for your data analysis and reporting needs.

The next set of R codes above performs the following actions:

  1. Loads the built-in iris dataset and optionally allows you to view its summary using tibble::glimpse(iris).

  2. You can uncomment the line # View(iris) to view the dataset in a separate window.

  3. Creates a scatter plot using ggplot2 to visualize the relationship between Sepal.Length and Sepal.Width.

  4. Imports the iris dataset from a CSV file located at “data/iris.csv” into a variable called iris_import using the read_csv function from the readr package.

  5. Exports the original iris dataset to a CSV file at the specified file path.

  6. The last comment mentions that you can use getwd() to show your current working directory path.

Please note that some lines of code are commented out and can be uncommented when needed.

3.11.3 Introduction to Jamovi

3.11.3.1 Overview of Jamovi Interface and Functionalities

Jamovi is a user-friendly statistical software with an intuitive interface. You can launch it by searching for “Jamovi” in your application menu.

3.11.3.1.1 Step 1: Launching Jamovi

  1. Open your web browser.

  2. In the address bar, type “https://www.jamovi.org/” and press Enter.

  3. On the Jamovi website, click on the “Download” or “Try Online” button to access Jamovi.

  4. If you choose to “Try Online,” it will open the Jamovi online interface in your browser.

3.11.3.1.2 Step 2: Interface Overview

  1. Familiarize yourself with the Jamovi interface.

    • The top menu contains options for File, Edit, View, Analysis, Data, and more.

    • The left panel displays the data set (if loaded) and variables.

    • The right panel shows the analysis output.

3.11.3.2 Importing Data and Basic Data Manipulation using Jamovi

3.11.3.2.1 Step 3: Importing Data

  1. In the left panel, under the “Data” tab, click “Import Dataset.”

  2. Choose the data file you want to import (e.g., CSV, Excel).

  3. Follow the on-screen instructions to configure data import settings and load your dataset.

3.11.3.2.2 Step 4: Basic Data Manipulation

  1. After loading the data, explore the “Data” tab on the left panel.

    • You can view and manipulate variables, including renaming, re-coding, or creating new variables.

  2. To perform basic data manipulation tasks:

    • Select variables by clicking on their names.

    • Use the right-click menu or the “Transform” option to apply changes.

3.11.3.2.3 Step 5: Saving Your Work

  1. To save your project:

    • Click on “File” in the top menu.

    • Select “Save Project As” and choose a location to save your .omv project file.

3.11.3.3 Introduction to Statistical Analyses in Jamovi

3.11.3.3.1 Step 6: Running Basic Analyses

  1. Under the “Analysis” tab in the top menu, you’ll find a wide range of statistical analyses.

  2. Select an analysis based on your research question (e.g., t-tests, ANOVA, regression).

  3. Configure the analysis by specifying variables, settings, and options.

  4. Click the “Run” button to execute the analysis.

3.11.3.3.2 Step 7: Interpreting Results

  1. After running an analysis, the results will appear in the right panel.

  2. Interpret the output, including statistical measures, p-values, and visualizations.

  3. Jamovi often provides descriptive statistics, charts, and inferential test results.

3.11.3.4 Statistical Analyses in Jamovi

Jamovi provides a wide range of statistical analyses, including t-tests, ANOVA, regression, and more. In the following sessions, we will explore these analyses in greater detail.

3.12 Software Integration

Jamovi, a user-friendly and open-source statistical analysis software, offers an interface that seamlessly integrates with R, a powerful programming language and environment for statistical computing. This integration combines the user-friendly features of Jamovi with the robust statistical capabilities of R, providing a flexible platform for data analysis and visualization.

Key points to consider in integrating R in Jamovi:

  1. Enhanced Statistical Power: Jamovi’s integration with R allows users to access a wide range of advanced statistical techniques and methods available in the R ecosystem. This includes specialized packages for complex data analysis and modeling.

  2. Interactive Analysis: Users can perform analyses in Jamovi using its point-and-click interface while observing the R syntax generated in real-time. This helps users learn and understand the R code associated with their analyses.

  3. Customization and Automation: For users familiar with R, the integration enables seamless customization and automation of analyses. R users can extend analyses conducted in Jamovi with additional scripting and package integration.

  4. Data Visualization: R’s data visualization capabilities are available within Jamovi, allowing users to create custom plots and charts for data exploration and presentation.

  5. Statistical Reporting: Users can generate reports in Jamovi, including statistical summaries, tables, and visualizations, which can be customized and exported for publication or sharing.

  6. Collaboration: Teams with varying levels of statistical expertise can collaborate effectively. Users can share Jamovi projects with colleagues, even if they are not R proficient, ensuring consistent analyses and results.

  7. Learning Opportunity: For those new to R, Jamovi serves as a valuable learning tool. Users can explore the R code generated by Jamovi, helping them transition to more extensive R-based analyses.

In essence, integrating R in Jamovi offers a powerful combination of user-friendly statistical analysis and the versatility of R scripting. It caters to both beginners and experienced statisticians, making it an ideal choice for data analysis, research, and collaboration across diverse domains.

3.12.1 R as a Backend for Jamovi

  1. R as a Backend: Jamovi, a user-friendly statistical analysis software, uses R as its computational backend. This means that when you perform statistical analyses or create plots in Jamovi, the software generates and executes corresponding R code in the background. This allows users who may not be familiar with R to take advantage of its powerful statistical capabilities.

  2. Point-and-Click Interface: Jamovi provides a point-and-click interface for performing statistical analyses. Users can easily import datasets, perform various statistical tests, create visualizations, and generate reports without writing any R code.

  3. Real-Time Syntax Generation: One of the key features of Jamovi is its ability to generate R syntax in real-time. As you perform actions in the Jamovi interface, such as running a t-test or creating a scatterplot, the corresponding R code is displayed. This provides users with a learning opportunity to understand the R commands associated with the analysis.

  4. Easy Transition to R: For users who want to transition to R or have specific customization needs, Jamovi simplifies the process. Users can copy the generated R syntax from Jamovi and use it directly in their R environment for further customization or scripting.

3.12.2 Integration of Jamovi in R

  1. R Packages for Jamovi: R users can take advantage of the “jmv” package, which allows them to interact with Jamovi directly from their R environment. This package provides functions to load Jamovi analyses, extract results, and incorporate Jamovi analyses into R scripts.

  2. Seamless Collaboration: Researchers or data analysts who prefer R can still collaborate effectively with colleagues or team members using Jamovi. They can create their analyses in Jamovi, export the results as datasets, and then use R for advanced statistical modeling or further data manipulation.

  3. Customization: R users can customize and extend the functionality of Jamovi analyses using R packages and scripts. This allows for greater flexibility and advanced data analysis when needed.

  4. Leveraging the Best of Both Worlds: The integration of Jamovi in R and R in Jamovi offers the best of both worlds. Users can enjoy the simplicity and user-friendly interface of Jamovi for routine analyses while harnessing the extensive statistical and data manipulation capabilities of R when required.

The integration of R in Jamovi and Jamovi in R provides users with a flexible and powerful ecosystem for conducting statistical analyses. It accommodates users of varying skill levels, from those who prefer a graphical interface to those who are experienced R users, facilitating effective collaboration and streamlined workflows in data analysis and research.

3.12.3 Setting up R Syntax Mode in Jamovi

Setting up R Syntax mode in Jamovi allows users to harness the full power of R programming within Jamovi’s user-friendly interface. This mode enables users to write, execute, and customize R code seamlessly while taking advantage of Jamovi’s data visualization and analysis features. Here’s how to set up R Syntax mode in Jamovi:

  1. Install Jamovi: If you haven’t already, download and install Jamovi on your computer from the official Jamovi website (https://www.jamovi.org/download.html).

  2. Launch Jamovi: Open Jamovi and create or open a dataset for analysis. You’ll typically start in the default point-and-click mode.

  3. Enable R Syntax Mode:

    • Navigate to the far end right corner of Jamovi window and click on the three vertical dots.

      3 dots

    • From the drop-down menu, select “R Syntax Mode.” This action switches your analysis interface to R Syntax mode.

      Syntax mode

  4. R Syntax Mode: Once you enable R Syntax Mode, you’ll notice that for any analysis or plotting, R codes will appear next to the results.

    syntax

  5. Writing R Code in Jamovi:

    • You can write and execute R codes directly from within Jamovi’s R editor. This is a module which is called “Rj” and can be accessed from the modules library. It must be installed and pinned to the main menu.

      Rj module

    • Click on the “Rj” icon and select “Rj editor”.

      rj editor

    • You can start writing R code directly in the console. For example, you can create variables, perform data manipulations, run statistical analyses, and create visualizations using R syntax. Examples are shown below.

      codes in Rj editor

  6. Running R Code: To execute the R code you’ve written, simply press the “Run” button in the R Syntax Console or use the shortcut (typically Ctrl+Shift+Enter or Cmd+Shift+Enter).

  7. Output and Visualizations: As you execute R code, any output, plots, or results will be displayed within the console. You can also create custom visualizations using R packages like ggplot2.

  8. Combining Point-and-Click and R: Jamovi’s unique feature allows you to switch between Point-and-Click mode and R Syntax mode seamlessly. You can start with a point-and-click analysis and switch to R Syntax mode to access advanced options and customization.

  9. Saving and Sharing: You can save your Jamovi project, which includes your dataset, analyses, and R code. This makes it easy to share your work or collaborate with others.

    save project or workspace (.omv)

    copy plots or results

  10. Learning Resources: If you’re new to R, there are plenty of online resources and tutorials available to help you learn R programming within Jamovi. Additionally, the generated R code can serve as a valuable learning tool.

Setting up R Syntax mode and Rj editor module in Jamovi empowers users to perform complex analyses and customizations, making it a versatile tool for both beginners and experienced data analysts and researchers. It combines the accessibility of Jamovi with the flexibility of R, offering the best of both worlds for data analysis and visualization.

3.12.4 Example:

3.12.4.1 Plotting

  1. Create a scatter-plot. The syntax should automatically be included in the result section along with plot. Right-click on the syntax area and select syntax to copy for use in R.syntax example
  2. In R, install and load the following packages: jmv and scatr. Furthermore, import the data set into R, paste the syntax copied over from Jamovi and run the syntax as shown below.
# Use pacman::p_load to load packages (jmv, scatr, jmvcore)
# with optional installation and no package updates
pacman::p_load(jmv, scatr, jmvcore, install = TRUE, update = FALSE)

# Import above-ground carbon data from a CSV or the SAV file
carbon <-
  readr::read_csv(file = here::here("docs", "data", "Filtered.csv"))

carbon_spss_data <-
  haven::read_sav(file = here::here("docs", "data", "Filtered.sav"))

# Syntax from the scatr package to create a scatterplot with linear regression lines
# This code visualizes the relationship between Tree Density, Aboveground Carbon, and Management Regime
scatr::scat(
  data = carbon,
  # Specify the dataset (carbon)
  y = "Aboveground_Tree_Carbon_ton_per_ha_per_year",
  # Choose the dependent variable (Y-axis)
  x = "Tree_Density_per_ha",
  # Choose the independent variable (X-axis)
  group = "Management_regime",
  # Group the data by Management Regime
  line = "linear",
  # Add linear regression lines
  se = TRUE
)                                              # Display standard error bars

R Code Explanation:

  • pacman::p_load(jmv, scatr, jmvcore, install = TRUE, update = FALSE) is used to load three packages: jmv, scatr, and jmvcore. The install = TRUE parameter ensures that these packages are installed if they are not already installed, and update = FALSE prevents the packages from being updated.

  • carbon <- readr::read_csv("./data/Filtered.csv") reads data from a CSV file named “Filtered.csv” located in the “./data” directory and stores it in a variable called “carbon.” This line imports the dataset needed for further analysis.

  • scatr::scat(...) is a function from the scatr package used to create a scatterplot with linear regression lines. The code specifies the dataset as “carbon,” sets the Y-axis variable to “Aboveground_Tree_Carbon_ton_per_ha_per_year,” sets the X-axis variable to “Tree_Density_per_ha,” groups the data by “Management_regime,” adds linear regression lines, and displays standard error bars. This code is used to visualize the relationship between Tree Density, Aboveground Carbon, and Management Regime in the dataset.

Note that plots created using the scatr package has limited functions to further tweak plots. A work around for this issue is to use the ggplot2 package which has more customizable functions. An example is shown below.

# Use pacman::p_load to load packages (ggthemes, ggplot2, patchwork)
# with optional installation and no package updates
pacman::p_load(ggthemes,
               ggplot2,
               patchwork,
               install = TRUE,
               update = FALSE)

# Import dataset from a CSV file
carbon <- readr::read_csv("./data/Filtered.csv")

# Create a customizable plot using ggplot2
plot1 <- ggplot2::ggplot(
  data = carbon,
  # Specify the dataset (carbon)
  aes(
    # Define aesthetic mappings
    x = carbon$Tree_Density_per_ha,
    # X-axis variable
    y = carbon$Aboveground_Tree_Carbon_ton_per_ha_per_year,
    # Y-axis variable
    col = carbon$Management_regime                           # Color by Management Regime
  )
) +
  ggplot2::geom_point(size = 3, pch = 21) +                  # Add points with custom size and shape
  ggplot2::geom_smooth(method = "lm") +                      # Add a linear regression line
  ggplot2::labs(x = "Tree density (ha)",                    # Set X-axis label
                y = "Above-ground tree carbon (tonne/ha/year)", # Set Y-axis label
                col = "Management Regime") +                 # Set legend title
  ggplot2::scale_x_continuous(limits = c(0, 1500)) +         # Set X-axis limits
  ggplot2::scale_y_continuous(limits = c(0, 6)) +            # Set Y-axis limits
  ggthemes::theme_base(base_size = 15, base_family = "times") +  # Apply custom theme settings
  ggplot2::theme(
    panel.grid.minor = element_line(size = 0.5, color = "grey"),
    # Customize minor grid lines
    axis.title = element_text(size = 20)                      # Customize axis title text
  )

# Print the customized plot
print(plot1)

R Code Explanation:

  • pacman::p_load(...) is used to load three packages: ggthemes, ggplot2, and patchwork. The install = TRUE parameter ensures that these packages are installed if they are not already installed, and update = FALSE prevents the packages from being updated.

  • carbon <- readr::read_csv("./data/Filtered.csv") reads data from a CSV file named “Filtered.csv” located in the “./data” directory and stores it in a variable called “carbon.” This line imports the dataset needed for plotting.

  • The ggplot2::ggplot(...) function is used to create a customizable plot. It specifies the dataset as “carbon” and defines aesthetic mappings, including X-axis, Y-axis, and color mapping based on the “Management_regime” column.

  • Various ggplot2::geom_ functions are used to add geometrical elements to the plot, such as points and a linear regression line.

  • ggplot2::labs(...), ggplot2::scale_..., and ggthemes::theme_... functions are used to customize plot labels, axis limits, and theme settings.

  • Finally, print(plot1) prints the customized plot to the output.

3.12.4.2 Combine multiple plots

# Modify the first plot (plot1)
p1 <- plot1 +
  ggplot2::labs(x = "Tree density (ha)",         # Change the X-axis label
                y = "Above-ground tree carbon (tonne/ha/year)",  # Change the Y-axis label
                col = "")                         # Remove the color legend title

# Create another customizable plot using ggplot2
plot2 <- ggplot2::ggplot(
  data = carbon,
  # Specify the dataset (carbon)
  aes(
    x = carbon$Management_regime,
    # X-axis variable
    y = carbon$Aboveground_Tree_Carbon_ton_per_ha_per_year  # Y-axis variable
  )
) +
  ggplot2::geom_boxplot(fill = "grey") +                  # Add a boxplot with grey fill
  ggplot2::labs(x = "Management Regime",                  # Set X-axis label
                y = "Above-ground tree carbon (tonne/ha/year)") +  # Set Y-axis label
  ggplot2::scale_y_continuous(limits = c(0, 6)) +         # Set Y-axis limits
  ggthemes::theme_base(base_size = 15, base_family = "times") +  # Apply custom theme settings
  ggplot2::theme(axis.title = element_text(size = 20))     # Customize axis title text

# Print the second plot (plot2)
print(plot2)

# Modify the second plot (plot2)
p2 <-
  plot2 + ggplot2::labs(x = "Management Regime",   # Change the X-axis label
                        y = "")                    # Remove the Y-axis label

# Combine both modified plots (p1 and p2) using the "&" operator
# Also, customize the legend position and add plot annotations
p1 + p2 & theme(legend.position = "bottom") &
  patchwork::plot_annotation(tag_levels = "a",
                             tag_prefix = "(",
                             tag_suffix = ")")

R Code Explanation:

  • p1 is created by modifying plot1. The X-axis label is changed, and the color legend title is removed.

  • plot2 is created as a new customizable plot using ggplot2. It specifies the dataset and aesthetic mappings, creates a box-plot, and customizes the plot labels, axis limits, and theme settings.

  • p2 is created by modifying plot2. The X-axis label is changed, and the Y-axis label is removed.

  • p1 + p2 & ... combines both modified plots p1 and p2 using the & operator. Additional customizations are applied to the combined plot, including changing the legend position and adding plot annotations with tags.

3.12.4.3 Analyses Syntax

The following syntax and results (image) below were generated in Jamovi. Syntax is further modified in R.

Analysis syntax and results from Jamovi.

# Load necessary R packages using pacman
pacman::p_load(jmv,          # Load the jmv package for statistical analysis
               magrittr,     # Load the magrittr package for data manipulation
               install = TRUE,  # Install packages if not already installed
               update = FALSE   # Do not update packages if newer versions are available
)

# Perform Kruskal-Wallis test with pairwise comparisons
kruskal_pairwise <- jmv::anovaNP(
    formula = Aboveground_Tree_Carbon_ton_per_ha_per_year ~ Plantation_age,  # Specify the formula
    data = carbon,                        # Specify the dataset (carbon)
    pairs = TRUE                          # Perform pairwise comparisons
)

# Display the Kruskal-Wallis significance test results
kruskal_pairwise %>% print()
## 
##  ONE-WAY ANOVA (NON-PARAMETRIC)
## 
##  Kruskal-Wallis                                                                  
##  ─────────────────────────────────────────────────────────────────────────────── 
##                                                   χ²          df    p            
##  ─────────────────────────────────────────────────────────────────────────────── 
##    Aboveground_Tree_Carbon_ton_per_ha_per_year    50.05889     7    < .0000001   
##  ─────────────────────────────────────────────────────────────────────────────── 
## 
## 
##  DWASS-STEEL-CRITCHLOW-FLIGNER PAIRWISE COMPARISONS
## 
##  Pairwise comparisons - Aboveground_Tree_Carbon_ton_per_ha_per_year 
##  ────────────────────────────────────────────────────────────────── 
##                W             p           
##  ────────────────────────────────────────────────────────────────── 
##    7     8     -5.0245113    0.0091010   
##    7     10    -0.4276180    0.9999889   
##    7     11     1.7104719    0.9296347   
##    7     12    -2.7795169    0.5055258   
##    7     17     1.2828540    0.9855155   
##    7     18     4.8107024    0.0154435   
##    7     21     4.2761799    0.0511307   
##    8     10     4.5968934    0.0254800   
##    8     11     4.7037979    0.0199077   
##    8     12     4.0623709    0.0783341   
##    8     17     5.3452248    0.0039229   
##    8     18     5.3452248    0.0039229   
##    8     21     5.3452248    0.0039229   
##    10    11     1.3897585    0.9769915   
##    10    12    -0.8552360    0.9988368   
##    10    17     2.1380899    0.8016074   
##    10    18     4.2761799    0.0511307   
##    10    21     4.4899889    0.0323768   
##    11    12    -2.8864214    0.4543784   
##    11    17     0.5345225    0.9999489   
##    11    18     4.3830844    0.0408393   
##    11    21     4.1692754    0.0635316   
##    12    17     3.3140394    0.2701716   
##    12    18     5.3452248    0.0039229   
##    12    21     4.7037979    0.0199077   
##    17    18     4.8107024    0.0154435   
##    17    21     4.0623709    0.0783341   
##    18    21     1.6035675    0.9494883   
##  ──────────────────────────────────────────────────────────────────

R Code Explanation:

  • pacman::p_load(...) is used to load the required R packages, including jmv for statistical analysis and magrittr for data manipulation. The install parameter is set to TRUE to install the packages if they are not already installed, and update is set to FALSE to prevent updating packages.

  • kruskal_pairwise stores the result of the Kruskal-Wallis test with pairwise comparisons. It calculates the Kruskal-Wallis test for the specified formula and dataset, and the pairs = TRUE argument indicates that pairwise comparisons should be performed.

  • kruskal_pairwise %>% print() is used to display the Kruskal-Wallis significance test results directly without the need to extract them into a data frame.

4 Chapter 2: Data Import and Cleaning

4.1 Introduction

Chapter 2 focuses on the critical aspects of data preparation for ecological data analysis. Here, you will learn how to efficiently import ecological datasets into R and Jamovi. Additionally, you’ll explore techniques for cleaning and preprocessing data, ensuring that your analyses are based on high-quality, error-free data. By the end of this chapter, you will have:

  • Acquired the skills to import data from various file formats.

  • Understood the importance of data cleaning and preprocessing.

  • Applied techniques to handle missing data, outliers, and data transformations.

4.2 Importing Data into R

4.2.1 Data Import Overview

Data import is a critical initial step in ecological research, as it involves bringing external data into your analysis environment (typically R or a similar software) for examination, manipulation, and analysis. The significance of data import in ecological research is multifaceted:

  1. Data Collection and Compilation: Ecological research often requires gathering data from various sources, such as field surveys, remote sensing, weather stations, or pre-existing databases. Data import is the process of bringing these diverse datasets together for a comprehensive analysis.

  2. Data Integration: Ecologists work with heterogeneous datasets, including numeric measurements, spatial coordinates, categorical variables, and textual descriptions. Data import allows you to integrate these diverse data types into a unified dataset, making it ready for analysis.

  3. Quality Assurance: Imported data may contain errors, missing values, outliers, or inconsistencies. During the import process, researchers can identify and address data quality issues, ensuring the integrity and reliability of subsequent analyses.

  4. Data Exploration: Once imported, data can be visualized and explored to gain insights into patterns, trends, and relationships. Effective data import facilitates initial exploratory data analysis (EDA), helping researchers decide on suitable statistical methods.

  5. Statistical Analysis: Ecological research often involves a wide range of statistical techniques, from simple descriptive statistics to advanced modeling. To apply these methods, data must be in a format that allows for statistical analysis, which data import achieves.

  6. Communication and Reporting: Accurate and well-organized data is crucial for communicating research findings to peers, policymakers, or the public. Data import ensures that data is in a format conducive to creating meaningful charts, graphs, and reports.

4.2.2 Common Data Sources in Ecological Research

  1. Field Surveys: Researchers collect primary data through field surveys, which can include measurements of species abundance, biodiversity, habitat characteristics, and environmental variables like temperature and precipitation.

  2. Remote Sensing: Satellite and aerial imagery, LiDAR (Light Detection and Ranging), and drones provide remote sensing data that can be used to monitor land cover, vegetation health, and changes in the environment over time.

  3. Climate and Weather Data: Climate and weather data, obtained from weather stations, are essential for studying the effects of climate change on ecosystems and wildlife behavior.

  4. Geospatial Data: Geographic Information Systems (GIS) data, including spatial coordinates, topography, and land use, are often used to study spatial patterns and relationships within ecosystems.

  5. Government Databases: Government agencies and organizations maintain extensive ecological datasets, including data on wildlife populations, conservation areas, and environmental regulations.

  6. Scientific Literature: Ecologists may extract data from published research papers or online databases, such as GenBank for genetic data or Global Biodiversity Information Facility (GBIF) for species occurrence records.

  7. Social Surveys: Ecological research may incorporate social surveys to assess human interactions with ecosystems, such as visitor behavior in national parks or community perceptions of environmental issues.

  8. Laboratory Experiments: Experimental data from controlled laboratory studies are used to investigate specific ecological hypotheses.

In summary, data import in ecological research serves as the gateway to the analysis and interpretation of complex ecological systems. It allows researchers to leverage diverse data sources, address data quality concerns, and ultimately gain a deeper understanding of the natural world.

4.2.3 Importing Flat Files (CSV and Excel)

# Load the readr package (if not already loaded)
library(readr)

# Set the file path to your CSV file
file_path <- "path/to/your/data.csv"

# Import the CSV file into a data frame
csv_data <- readr::read_csv(file_path)

# View the imported data
head(csv_data)

# Load the readxl package (if not already loaded)
library(readxl)

# Set the file path to your Excel file
file_path <- "path/to/your/data.xlsx"

# Import the Excel file into a data frame (assuming the data is in the first sheet)
xlsx_data <- readxl::read_excel(file_path, sheet = 1)

# View the imported data
head(xlsx_data)

R Code Explanation:

  • For Importing a CSV File:

  1. Load the readr Package: This line (line 2) loads the readr package, which is used for reading CSV files.

  2. Set the File Path: In line 5, you need to set the file path to your CSV data file. Replace "path/to/your/data.csv" with your actual file path.

  3. Import the CSV File: Line 8 uses the read_csv function from the readr package to read the CSV file specified by file_path and stores it in the csv_data data frame.

  4. View the Imported Data: Line 11 displays the first few rows of the imported CSV data using the head function, allowing you to inspect the data.

  • For Importing an Excel File:

  1. Load the readxl Package: This line (line 14) loads the readxl package, which is used for reading Excel files.

  2. Set the File Path: In line 17, you should set the file path to your Excel data file. Replace "path/to/your/data.xlsx" with your actual file path.

  3. Import the Excel File: Line 20 uses the read_excel function from the readxl package to read the Excel file specified by file_path. The imported data is stored in the xlsx_data data frame.

  4. View the Imported Data: Line 23 displays the first few rows of the imported Excel data using the head function for initial data exploration.

These steps guide you through the process of importing data from CSV and Excel files into R, allowing you to work with your ecological datasets. Remember to replace the file paths with your actual file paths when applying these steps in your R script or environment.

4.2.4 Importing Data from Databases (e.g., SQL Databases)

# Load the DBI and odbc packages (if not already loaded)
library(DBI)
library(odbc)

# Define the database connection details
db_connection <- dbConnect(
  odbc::odbc(),
  Driver = "Your_Database_Driver",
  # e.g., "SQL Server" or "PostgreSQL"
  Server = "Your_Server_Address",
  Database = "Your_Database_Name",
  UID = "Your_Username",
  PWD = "Your_Password"
)

# Check the database connection
dbIsValid(db_connection)

# Specify the SQL query to retrieve data from a table
sql_query <- "SELECT * FROM Your_Table_Name"

# Execute the SQL query and import the data into a data frame
db_data <- dbGetQuery(db_connection, sql_query)

# View the imported data
head(db_data)

R Code Explanation:

  1. Load DBI and odbc Packages:

    • These lines load the necessary R packages for working with databases. DBI is a database interface, and odbc is a package for database connectivity.

  2. Define the Database Connection Details:

    • db_connection <- dbConnect(odbc::odbc(), ...) sets up a connection to a database. You need to specify details such as the database driver, server address, database name, username, and password.

    • Replace "Your_Database_Driver", "Your_Server_Address", "Your_Database_Name", "Your_Username", and "Your_Password" with your actual database information.

  3. Check the Database Connection:

    • dbIsValid(db_connection) verifies if the database connection is valid. It will return TRUE if the connection is successful.

  4. Specify the SQL Query:

    • sql_query <- "SELECT * FROM Your_Table_Name" sets up an SQL query to retrieve data from a specific table in your database.

    • Replace "Your_Table_Name" with the actual name of the table you want to query.

  5. Execute the SQL Query and Import Data:

    • db_data <- dbGetQuery(db_connection, sql_query) executes the SQL query on the database server and imports the result into an R data frame called db_data.

  6. View the Imported Data:

    • head(db_data) displays the first few rows of the imported data frame, allowing you to inspect the data.

These codes are used to establish a connection to a database, retrieve data from it using an SQL query, and bring that data into R for further analysis. Remember to replace the placeholders with your actual database information.

Note that structured data management is of paramount importance in ecological research, and here’s why it deserves special attention:

  1. Data Quality Assurance: Structured data management ensures that the data you work with is accurate, reliable, and consistent. This includes addressing issues like missing values, outliers, duplicates, and data entry errors. High-quality data is essential for making sound ecological inferences and drawing reliable conclusions.

  2. Data Integrity: Managing data in a structured manner preserves its integrity throughout the research process. It reduces the risk of inadvertent changes, deletions, or overwrites that can compromise the reliability of your findings.

  3. Reproducibility: Structured data management facilitates research reproducibility. When others attempt to replicate your research or when you revisit your own work after some time, well-structured data ensures that you can easily understand, replicate, and build upon your previous analyses.

  4. Data Traceability: Structured data management often involves proper documentation of data sources, collection methods, and transformations. This traceability is critical for establishing the credibility and transparency of your research.

  5. Efficient Analysis: Structured data is easier to work with, reducing the time and effort required for data cleaning, preprocessing, and analysis. Researchers can focus on the ecological questions and insights rather than wrestling with messy data.

  6. Collaboration: If your research involves collaboration with other researchers or teams, structured data management becomes indispensable. It ensures that everyone is on the same page regarding data formats, variable definitions, and data handling protocols.

  7. Long-Term Data Preservation: Ecological research often spans long periods. Properly structured data ensures that data can be preserved and reused over time, even as technology and personnel change.

  8. Data Sharing and Accessibility: In many cases, ecological research data is of broader interest and value to the scientific community, policymakers, and conservationists. Well-structured data can be more easily shared, reused, and made accessible to a wider audience.

  9. Statistical Analysis: Structured data is a prerequisite for conducting meaningful statistical analyses. Many statistical tools and software packages require data to be organized in a particular format. Structured data management ensures that your data is analysis-ready.

  10. Ethical Considerations: Ethical research practices often include data protection and privacy considerations. Structured data management helps in anonymizing and securing sensitive data as needed, ensuring compliance with ethical guidelines.

In summary, structured data management is the foundation upon which ecological research is built. It ensures data quality, facilitates analysis, promotes transparency, and enhances the overall credibility and impact of your research. Researchers who invest in structured data management are better equipped to make significant contributions to the understanding and conservation of ecosystems.

4.3 Importing Data into Jamovi

4.3.1 Jamovi Data Import

Jamovi simplifies data import with its user-friendly interface, making it accessible to users who may not be familiar with coding or complex data manipulation.

  • Importing CSV and Excel Files in Jamovi

import data

4.4 Data Cleaning

4.4.1 Data Cleaning Overview

Data cleaning is of paramount significance in ecological analysis due to its substantial impact on research outcomes. Here’s why data cleaning is essential in ecological research:

  1. Data Quality Assurance: Raw ecological data often contain errors, inaccuracies, or inconsistencies due to various factors, such as measurement errors, sensor malfunctions, or human errors during data collection. Data cleaning is the process of identifying and rectifying these issues, ensuring that the data accurately represent the ecological phenomena under study.

  2. Accurate Analyses: Cleaned data provide a reliable foundation for statistical analyses and modeling. Without data cleaning, the results of analyses may be misleading or erroneous, potentially leading to incorrect conclusions about ecological relationships or trends.

  3. Reducing Bias: Incomplete or erroneous data can introduce bias into research outcomes. Data cleaning helps reduce this bias, ensuring that the results are more representative of the true ecological conditions.

  4. Enhanced Interpretability: Cleaned data are easier to interpret and visualize. Researchers can trust that patterns and relationships observed in the data are genuine and not artifacts of data errors or anomalies.

  5. Effective Data Visualization: Data cleaning improves the quality of data visualization. Visualizations, such as graphs and charts, are crucial for conveying ecological findings. Cleaned data enable researchers to create informative and accurate visual representations.

  6. Comparability: Cleaned data allow for meaningful comparisons within and between ecological studies. Researchers can confidently compare data from different sources or time periods, knowing that data quality issues have been addressed.

  7. Scientific Credibility: Ecological research relies on the credibility of findings. Cleaned data enhance the scientific rigor of a study, increasing confidence in its results and conclusions.

  8. Effective Decision-Making: Ecological research often informs conservation efforts, policy decisions, and resource management. Cleaned data ensure that decisions made based on research outcomes are well-founded and have a positive impact on ecosystems and biodiversity.

  9. Data Archiving: High-quality, cleaned data are more suitable for long-term archiving and sharing with the scientific community. Properly cleaned and documented data sets can contribute to broader ecological knowledge and support future research.

  10. Time and Resource Efficiency: Although data cleaning requires effort, it ultimately saves time and resources during analysis. Cleaned data lead to more efficient and accurate statistical procedures.

In ecological analysis, where data are collected in diverse and often challenging environments, data cleaning is a critical step in the research process. It transforms raw, potentially problematic data into a reliable foundation for meaningful analysis, interpretation, and the generation of ecological insights that contribute to our understanding of the natural world.

4.4.2 Handling Missing Data

Handling missing data in ecological research is crucial to ensure the integrity and validity of your analyses. Here are techniques for identifying and handling missing data:

  1. Identifying Missing Data:

    • Summary Statistics: Calculate summary statistics such as mean, median, and standard deviation for each variable. Missing data will be indicated by “NA” or “NaN” values in R or blank cells in spreadsheets.

    • Visualization: Create visualizations like histograms or bar plots to visualize the distribution of missing data for each variable. This can reveal patterns of missingness.

    • Missing Data Packages: R packages like naniar, skimr or VIM provide functions and plots specifically designed for visualizing and understanding missing data patterns.

  2. Handling Missing Data:

    • Removal: Sometimes, the simplest approach is to remove observations (rows) or variables (columns) with missing data. However, this should be done judiciously, as it can lead to loss of valuable information.

    • Imputation: Imputation involves estimating missing values based on observed data. Common imputation methods include mean imputation (replacing missing values with the mean of the variable), median imputation, or regression imputation (predicting missing values based on other variables). R packages like mice and missForest provide powerful imputation tools.

    • Data Augmentation: In Bayesian statistics, data augmentation techniques can be used to account for missing data by treating them as additional parameters to be estimated.

    • Interpolation/Extrapolation: In time series or spatial data, missing values can often be estimated through interpolation (estimating values within the range of observed data) or extrapolation (estimating values beyond the range of observed data).

    • Multiple Imputation: This advanced technique involves creating multiple datasets with different imputed values for missing data and analyzing each dataset separately. Results are then combined to account for uncertainty due to missing data. The mice package in R is commonly used for multiple imputation.

  3. Exploring Patterns of Missing Data:

    • Missing Data Heatmaps: Use heat-maps to visualize the patterns of missing data in your dataset. This helps identify if missingness is random or if there are systematic patterns related to specific variables or time periods.

    • Missing Data by Subgroup: Explore if missingness varies by subgroups within your data (e.g., by location, species, or time). Understanding these patterns can inform imputation strategies.

    • Missing Data Mechanisms: Consider the mechanism behind missing data. Is it missing completely at random (MCAR), missing at random (MAR), or not missing at random (NMAR)? This information can guide imputation methods.

    • Sensitivity Analysis: Perform sensitivity analyses to assess how different imputation methods or missing data assumptions impact your results. This helps quantify the uncertainty associated with missing data.

    • Collect More Data: In some cases, the best solution is to collect more data to reduce missingness in critical variables.

Remember that there is no one-size-fits-all approach to handling missing data in ecological research. The choice of method should depend on the nature of the data, the extent of missingness, and the goals of your analysis. Transparently report your methods for handling missing data in research publications to ensure the reproducibility of your findings.

4.4.3 Outlier Detection and Treatment

Outliers are data points that significantly deviate from the rest of the data in a dataset. Detecting and addressing outliers is essential in ecological research for several reasons:

  • Importance of Addressing Outliers:

  1. Influence on Statistics: Outliers can strongly influence summary statistics like the mean and standard deviation, leading to biased estimates. This can affect the interpretation of ecological patterns and relationships.

  2. Model Assumptions: Many statistical models assume that the data follow a certain distribution or have homogeneous variances. Outliers violate these assumptions, potentially leading to incorrect model inferences.

  3. Ecological Significance: Outliers may represent rare or unusual ecological events that are of particular interest or concern. Identifying and understanding these outliers can be critical for ecological research.

  • Methods for Detecting Outliers:

  1. Visual Inspection: The simplest method is to create visualizations like scatter plots, box plots, or histograms. Outliers often appear as data points far from the main cluster or as individual points outside the whiskers of a box plot.

  2. Z-Scores: Calculate the Z-score for each data point, which measures how many standard deviations a data point is from the mean. Data points with Z-scores beyond a certain threshold (e.g., |Z| > 2 or 3) are considered outliers.

  3. Tukey’s Method: Tukey’s method uses the Interquartile Range (IQR) to detect outliers. Data points outside the range defined by Q1 - 1.5 * IQR and Q3 + 1.5 * IQR are considered outliers, where Q1 and Q3 are the first and third quartiles, respectively.

  4. Modified Z-Scores: In cases where data are not normally distributed, modified Z-scores like the Median Absolute Deviation (MAD) can be more robust for outlier detection.

  • Techniques for Outlier Treatment:

  1. Removal: The simplest approach is to remove outliers from the dataset. However, this should be done cautiously and with justification, as removing data points can lead to information loss.

  2. Transformation: Transforming the data using mathematical functions (e.g., logarithm) can reduce the impact of outliers and make the data more amenable to analysis.

  3. Winsorization: Winsorization replaces extreme values with values closer to the rest of the data (e.g., setting all values above a certain threshold to that threshold). This approach preserves the data distribution while mitigating the influence of outliers.

  4. Robust Statistical Methods: Robust statistical methods, such as robust regression or robust estimation of central tendency and variance, are less influenced by outliers and provide more reliable estimates.

  5. Modeling Approaches: In some cases, it may be appropriate to model outliers explicitly as a separate group or to use models that are robust to outliers.

  6. Reporting: Regardless of the approach chosen, it is essential to transparently report how outliers were handled in research publications to ensure the reproducibility and credibility of the analysis.

The choice of outlier detection and treatment methods should depend on the nature of the data and the research objectives. It is advisable to perform sensitivity analyses to assess how different outlier strategies impact research findings.

4.5 Data Preprocessing

4.5.1 Data Preprocessing Overview

Data preprocessing refers to a set of procedures and techniques used to clean, transform, and prepare raw data for analysis. It plays a pivotal role in the data analysis process, as the quality and structure of the data significantly influence the outcomes of statistical analyses and machine learning models.

The key steps in data preprocessing include data cleaning (dealing with missing values and outliers), data transformation (changing the format or distribution of data), and data reduction (reducing the volume but preserving the key information). Data preprocessing aims to ensure that the data is in a suitable form for analysis, making it more interpretable and increasing the accuracy and reliability of analytical results.

4.5.1.1 Data Transformation

Data transformation involves altering the data values to meet the assumptions of statistical analysis. Various data transformation techniques can be applied in ecological research:

  1. Log Transformation: Logarithmic transformation is commonly used to stabilize variance, make the data more symmetric, and approximate a normal distribution. It is particularly useful when dealing with data that exhibit exponential growth or decay, such as species abundance data or tree growth rates.

  2. Square Root Transformation: Similar to log transformation, square root transformation can be used to stabilize variance and approximate normality. It is effective when dealing with count data or data with non-constant variance.

  3. Box-Cox Transformation: The Box-Cox transformation is a family of power transformations that can be applied to make data conform to normality assumptions. It includes both logarithmic and square root transformations as special cases. The optimal transformation is selected based on maximum likelihood estimation.

  4. Arcsine Transformation: Arcsine square root transformation is used for proportional data or data with bounded values (e.g., percentage data). It can make the data more symmetric and suitable for parametric tests.

  5. Exponential Transformation: When dealing with data that follows a decay process, an exponential transformation can be applied to linearize the relationship.

4.5.1.1.1 When to Apply Data Transformations

Data transformations should be applied when:

  • Data violate assumptions of normality or homoscedasticity required for parametric tests.

  • Data exhibit heteroscedasticity (variance changes with the level of a variable).

  • The research question or theoretical considerations suggest that a particular transformation is appropriate (e.g., log-transforming biomass data).

4.5.1.1.2 Improvement of Normality and Homoscedasticity

Data transformations can improve normality by reducing skewness and kurtosis in the data distribution. Normality is essential for parametric tests like t-tests and ANOVA, which assume that data follow a normal distribution.

Transformations can also help in achieving homoscedasticity, where the variance of the residuals is constant across levels of an independent variable. This is crucial for linear regression and ANOVA, as violations of homoscedasticity can lead to incorrect inferences.

4.5.2 Scaling and Centering

  • Scaling: Scaling variables involves transforming them to have a common scale or range, typically between 0 and 1 or with a mean of 0 and a standard deviation of 1. Scaling is essential when variables have different units or scales because it ensures that all variables contribute equally to analyses like clustering or principal component analysis.

  • Centering: Centering involves subtracting the mean of a variable from each data point. Centering is useful when interpreting regression coefficients because it makes the intercept more interpretable. In the context of multiple regression, centering can reduce multicollinearity between predictor variables.

4.5.2.1 Why Scaling Is Essential for Variables with Different Units

When variables have different units or scales, their magnitudes can dominate the results of certain analyses. Scaling ensures that all variables are treated equally, preventing larger variables from unduly influencing the outcomes. It also facilitates the interpretation of coefficients in regression models because the coefficients represent the effect of a one-unit change in the predictor variable while holding other variables constant. Scaling ensures that this one-unit change is consistent across all predictors, regardless of their units or scales.

4.6 Conclusion

Chapter 2 of “Exploring Ecological Data with R and Jamovi” emphasizes the critical importance of successful data import, cleaning, and preprocessing in ecological data analysis. Here are the key takeaways:

  1. Data Import Significance: Data import is the initial step in any data analysis project. Ecological researchers often deal with diverse data sources, including flat files (e.g., CSV, Excel) and databases. Accurate data import ensures that you have access to the necessary information for analysis.

  2. Common Data Sources: Ecological research commonly involves data from various sources, including field observations, experiments, and remote sensing. Understanding how to import data from these sources is essential for ecologists.

  3. R and Jamovi Integration: Both R and Jamovi offer user-friendly approaches to data import. Jamovi provides a point-and-click interface, while R offers versatile functions like readr and readxl for importing data from flat files.

  4. Database Connection: For larger datasets stored in relational databases, knowing how to connect to and import data from databases is crucial. R provides packages like DBI and odbc for this purpose.

  5. Structured Data Management: Structured data management ensures that your data is organized, consistent, and error-free. This process involves tasks such as handling missing data, identifying and treating outliers, and transforming data when necessary.

  6. Missing Data Handling: Missing data can impact the validity of your analyses. Techniques like data imputation, removal of missing values, and exploring patterns of missingness are essential for handling missing data effectively.

  7. Outlier Detection and Treatment: Outliers can distort statistical analyses and lead to inaccurate conclusions. Visual inspection, Z-scores, and Tukey’s method are valuable tools for identifying and addressing outliers.

  8. Data Transformation: Data transformation techniques like log transformation, square root transformation, and Box-Cox transformation can help meet assumptions of normality and homoscedasticity, improving the reliability of statistical analyses.

  9. Scaling and Centering: Scaling variables to a common range and centering variables around their mean are important for ensuring that variables with different units or scales are treated equally in analyses.

  10. Key Emphasis: Successful data import, cleaning, and preprocessing are essential steps to ensure that ecological analyses are based on accurate and reliable data. These steps lay the foundation for meaningful and trustworthy research outcomes.

By mastering these data management techniques, you are now well-prepared to explore and analyze ecological datasets with confidence, setting the stage for robust ecological research.

5 Chapter 3: Exploratory Data Analysis (EDA)

5.1 Introduction

In Chapter 3, you will embark on a journey into the world of Exploratory Data Analysis (EDA) for ecological data. EDA is a crucial step that allows you to understand and gain insights from your datasets before diving into formal statistical analyses. By the end of this chapter, you will have:

  • Mastered various visualization techniques for ecological data.

  • Learned how to summarize and describe your data effectively.

  • Discovered patterns, relationships, and outliers within your datasets.

5.2 The Importance of EDA

5.2.1 Understanding EDA

Exploratory Data Analysis (EDA) is a critical phase in the data analysis process that involves the initial examination, visualization, and summary of data. It serves as a fundamental tool in ecological research and data analysis. Here’s an explanation of the concept and its significance in ecological research:

5.2.1.1 Concept of EDA

  • EDA is an approach used to understand the main characteristics of a dataset before applying more complex statistical methods.

  • It aims to uncover patterns, relationships, anomalies, and other insights within the data.

  • EDA employs a combination of graphical and numerical techniques to achieve these objectives.

  • It is a crucial step in the data analysis pipeline, allowing researchers to formulate hypotheses and make informed decisions about subsequent analyses.

5.2.1.2 Significance of EDA in Ecological Research

  • Ecological datasets are often complex and multidimensional, containing numerous variables and data points.

  • EDA helps researchers gain an initial understanding of the dataset’s structure and content.

  • It aids in identifying potential data quality issues such as outliers, missing values, or data inconsistencies.

  • EDA enables the discovery of trends and patterns within ecological data, which can guide further analysis.

  • Through visualization, EDA helps in the communication of results to both scientific and non-scientific audiences.

  • EDA can highlight relationships between ecological variables, supporting the formulation of research questions and hypotheses.

  • In ecological research, where the influence of environmental factors on ecosystems is studied, EDA is crucial for uncovering insights that can drive conservation efforts and environmental management decisions.

5.2.2 EDA Workflow

The typical workflow of an EDA process in ecological research involves the following steps:

  1. Data Collection: Gather ecological data from various sources, such as field surveys, experiments, or remote sensing.

  2. Data Cleaning and Preprocessing: As discussed in Chapter 2, prepare the data by handling missing values, identifying and treating outliers, and performing necessary data transformations.

  3. Univariate Analysis: Begin with a univariate analysis, which involves exploring each variable individually. Compute summary statistics, generate histograms, density plots, and box plots to understand the distribution and central tendency of each variable.

  4. Bivariate Analysis: Move on to bivariate analysis to examine relationships between pairs of variables. Scatter plots, correlation matrices, and cross-tabulations can reveal associations between ecological factors.

  5. Multivariate Analysis: Explore relationships involving multiple variables simultaneously. Techniques like principal component analysis (PCA) or multidimensional scaling (MDS) can provide insights into complex data structures.

  6. Visualization: Utilize data visualization tools, such as scatter plots, bar charts, heat-maps, and spatial maps, to create visual representations of ecological patterns and trends.

  7. Hypothesis Generation: Based on insights gained from EDA, generate hypotheses about ecological processes, interactions, or correlations that warrant further investigation.

  8. Summary and Reporting: Summarize key findings and insights from the EDA process. Create reports, presentations, or visuals to communicate the results to stakeholders, colleagues, or the broader scientific community.

  9. Iterative Process: EDA is often iterative, as insights from initial analysis may lead to further questions or refinements in subsequent analyses.

In ecological research, EDA serves as a powerful tool for uncovering hidden insights within complex datasets, guiding subsequent analyses, and informing ecological decision-making processes. It enables researchers to make data-driven conclusions and contributes to a deeper understanding of ecological systems and environmental dynamics.

5.3 Data Visualization

5.3.1 Data Visualization Overview

Data visualization is a cornerstone of Exploratory Data Analysis (EDA) in ecological research. It is a powerful technique that allows researchers to represent complex data visually, making it easier to understand and interpret. Here’s an overview of the significance of data visualization in EDA:

  • Understanding Complex Data: Ecological datasets often contain numerous variables and data points. Visualization provides a means to simplify complex data structures and reveal patterns, trends, and relationships that might be hidden in raw numbers.

  • Quality Assessment: Visualization aids in identifying data quality issues, such as outliers, missing values, and anomalies. Visual cues can highlight problematic data points for further investigation.

  • Hypothesis Generation: Visual exploration of data can spark hypotheses and research questions. Researchers can form initial insights into ecological processes and phenomena, guiding subsequent analyses.

  • Effective Communication: Visual representations of data are powerful tools for communicating research findings to both scientific and non-scientific audiences. Clear and compelling visuals enhance the impact of ecological research.

Now, let’s delve into various aspects of data visualization, including univariate, bivariate, and multivariate visualization techniques, using the CO2 dataset in R.

5.3.2 Univariate Visualization

Univariate visualization focuses on visualizing single variables to understand their distributions and characteristics. Here are some common techniques and interpretations:

  • Histograms: Histograms display the frequency distribution of a single variable. They help visualize the shape (e.g., normal, skewed) and central tendency (e.g., mean, median) of the data.
# Load the CO2 dataset
data("CO2")

# Create a histogram of CO2 uptake
hist(CO2$uptake, main = "Histogram of CO2 Uptake", xlab = "CO2 Uptake")

R Code Explanation

  • data("CO2") loads the built-in CO2 dataset into your R environment. This dataset contains measurements related to the uptake of carbon dioxide (CO2) by different plants under varying conditions.

  • hist(CO2$uptake, ...) creates a histogram of the “uptake” variable within the CO2 dataset. Specifically:

    • CO2$uptake extracts the “uptake” column (variable) from the CO2 dataset, which represents the CO2 uptake measurements.

    • hist(...) is the function used to create histograms in R.

  • main = "Histogram of CO2 Uptake" specifies the main title of the histogram, which is displayed at the top of the plot. In this case, it’s titled “Histogram of CO2 Uptake.”

  • xlab = "CO2 Uptake" labels the x-axis of the histogram, providing a description of what the x-axis represents. Here, it indicates that the x-axis represents CO2 uptake.

This code, when executed, will load the CO2 dataset and then generate a histogram showing the distribution of CO2 uptake measurements. The histogram’s title will be “Histogram of CO2 Uptake,” and the x-axis will be labeled “CO2 Uptake,” making the plot informative and easy to understand.

  • Density Plots: Density plots provide smoothed representations of data distributions. They are useful for visualizing data density and identifying modes (peaks) in the distribution.
# Create a density plot of CO2 uptake
plot(density(CO2$uptake), main = "Density Plot of CO2 Uptake", xlab = "CO2 Uptake")

R Code Explanation

  • plot(density(CO2$uptake), ...) creates a density plot (also known as a kernel density plot) of the “uptake” variable within the CO2 dataset. Specifically:

    • density(CO2$uptake) calculates the density estimate for the “uptake” variable, representing the distribution of CO2 uptake measurements. This estimate is what the density plot will be based on.

    • plot(...) is used to create plots in R.

  • main = "Density Plot of CO2 Uptake" specifies the main title of the density plot, which is displayed at the top of the plot. In this case, it’s titled “Density Plot of CO2 Uptake.”

  • xlab = "CO2 Uptake" labels the x-axis of the density plot, providing a description of what the x-axis represents. Here, it indicates that the x-axis represents CO2 uptake.

When this code is executed, it will calculate the density estimate of CO2 uptake measurements and create a density plot to visualize the distribution. The main title will be “Density Plot of CO2 Uptake,” and the x-axis will be labeled “CO2 Uptake,” making the plot informative and easy to interpret.

  • Box Plots: Box plots summarize the distribution of a variable, showing its median, quartiles, and potential outliers. They are effective for identifying skewness and outlier presence.
# Create a box plot of CO2 uptake
boxplot(CO2$uptake, main = "Box Plot of CO2 Uptake", xlab = "CO2 Uptake")

R Code Explanation

  • boxplot(CO2$uptake, ...) creates a box plot of the “uptake” variable within the CO2 dataset. Specifically:

    • CO2$uptake specifies the variable to be plotted, which is CO2 uptake in this case.

  • main = "Box Plot of CO2 Uptake" specifies the main title of the box plot, which is displayed at the top of the plot. In this case, it’s titled “Box Plot of CO2 Uptake.”

  • xlab = "CO2 Uptake" labels the x-axis of the box plot, providing a description of what the x-axis represents. Here, it indicates that the x-axis represents CO2 uptake.

When this code is executed, it will create a box plot of the CO2 uptake variable, allowing you to visualize the distribution of CO2 uptake measurements. The main title will be “Box Plot of CO2 Uptake,” and the x-axis will be labeled “CO2 Uptake,” making the plot informative and easy to interpret. Box plots are useful for visualizing the spread and central tendency of a dataset, as well as identifying potential outliers.

5.3.3 Bivariate Visualization

Bivariate visualization involves exploring relationships between two variables. Here are some techniques and their interpretations:

  • Scatter Plots: Scatter plots display the relationship between two continuous variables. They can reveal patterns, correlations, and potential outliers.
# Create a scatter plot of CO2 uptake vs. CO2 concentration
plot(CO2$conc,
     CO2$uptake,
     main = "Scatter Plot of CO2 Uptake vs. CO2 Concentration",
     xlab = "CO2 Concentration",
     ylab = "CO2 Uptake")

R Code Explanation

  • plot(CO2$conc, CO2$uptake, ...) creates a scatter plot with CO2 concentration (x-axis) on one axis and CO2 uptake (y-axis) on the other. Specifically:

    • CO2$conc specifies the variable to be plotted on the x-axis, which is CO2 concentration.

    • CO2$uptake specifies the variable to be plotted on the y-axis, which is CO2 uptake.

  • main = "Scatter Plot of CO2 Uptake vs. CO2 Concentration" specifies the main title of the scatter plot. In this case, it’s titled “Scatter Plot of CO2 Uptake vs. CO2 Concentration.”

  • xlab = "CO2 Concentration" labels the x-axis of the scatter plot, providing a description of what the x-axis represents. Here, it indicates that the x-axis represents CO2 concentration.

  • ylab = "CO2 Uptake" labels the y-axis of the scatter plot, providing a description of what the y-axis represents. Here, it indicates that the y-axis represents CO2 uptake.

When this code is executed, it will create a scatter plot that allows you to visualize the relationship between CO2 concentration and CO2 uptake. The main title will be “Scatter Plot of CO2 Uptake vs. CO2 Concentration,” and both the x-axis and y-axis will be appropriately labeled, making the plot informative and easy to interpret. Scatter plots are useful for identifying patterns and relationships between two continuous variables.

  • Bar Charts: Bar charts are useful for visualizing the distribution of a categorical variable or the relationship between a categorical variable and a continuous variable.
# Create a bar chart of Plant types
barplot(table(CO2$Type),
        main = "Bar Chart of Plant Types",
        xlab = "Type",
        ylab = "Frequency")

R Code Explanation

  • barplot(table(CO2$Type), ...) creates a bar chart of plant types based on the CO2$Type variable. Specifically:

    • table(CO2$Type) computes a frequency table of the plant types in the CO2 dataset. It counts how many times each unique plant type appears.

    • barplot(...) takes the frequency table as input and generates a bar chart from it.

  • main = "Bar Chart of Plant Types" specifies the main title of the bar chart. In this case, it’s titled “Bar Chart of Plant Types.”

  • xlab = "Type" labels the x-axis of the bar chart, providing a description of what the x-axis represents. Here, it indicates that the x-axis represents different plant types.

  • ylab = "Frequency" labels the y-axis of the bar chart, providing a description of what the y-axis represents. Here, it indicates that the y-axis represents the frequency (count) of each plant type.

When this code is executed, it will create a bar chart that visually displays the frequency of each plant type in the CO2 dataset. The main title will be “Bar Chart of Plant Types,” and both the x-axis and y-axis will be appropriately labeled, making the chart informative and easy to interpret. Bar charts are useful for comparing categories or groups by showing the frequency or count of each category.

  • Correlation Plots: Correlation plots, such as heatmaps or scatterplot matrices, show the pairwise relationships between multiple continuous variables. They help identify correlations and dependencies among variables.
# Compute the correlation matrix
cor_matrix <- cor(CO2[, c("uptake", "conc")])

# Create a correlation heatmap
heatmap(cor_matrix, main = "Correlation Heatmap")

R Code Explanation

  • heatmap(...) generates a heatmap (a graphical representation of data in which values are depicted as colors) based on the correlation matrix provided as input. Here’s how it’s used in this code:

    • cor_matrix is the correlation matrix we computed earlier, containing the correlation coefficients between “uptake” and “conc.”

    • main = "Correlation Heatmap" specifies the main title of the heatmap. In this case, it’s titled “Correlation Heatmap.”

When this code is executed, it will create a heatmap that visually represents the correlations between the “uptake” and “conc” variables from the CO2 dataset. The heatmap’s colors and intensity will indicate the strength and direction of the correlations between these variables. It provides a quick and informative way to assess the relationships between variables in a dataset.

5.3.4 Multivariate Visualization

Multivariate visualization techniques allow researchers to analyze interactions among multiple variables. Here’s an example:

  • Heatmaps: Heatmaps are effective for visualizing relationships between multiple variables, especially in ecological studies where datasets are multidimensional. They provide a comprehensive view of correlations or patterns.
# Load the corrplot package for enhanced heatmap visualization
library(corrplot)
## corrplot 0.92 loaded
# Load data
data("iris")

# Compute the correlation matrix
cor_matrix2 <-
  cor(iris[, c("Petal.Length", "Petal.Width", "Sepal.Length", "Sepal.Width")])

# Create a correlation heatmap for multiple variables
corrplot(cor_matrix2, method = "color", title = "Correlation Heatmap")

R Code Explanation

  • library(corrplot) loads the corrplot package, which provides enhanced capabilities for visualizing correlation matrices.

  • data("iris") loads the famous “iris” dataset, which contains measurements of sepal and petal length and width for different species of iris flowers. This dataset is used for the correlation analysis.

  • cor(...) calculates the correlation coefficients between variables. In this case, it calculates the correlation coefficients between four variables: “Petal.Length,” “Petal.Width,” “Sepal.Length,” and “Sepal.Width.” The resulting cor_matrix2 is a 4x4 correlation matrix, where each entry represents the correlation between two variables.

  • corrplot(...) from the corrplot package generates a correlation heatmap based on the correlation matrix provided as input (cor_matrix2). Here’s how it’s used in this code:

    • method = "color" specifies the method for displaying the correlations using colors. This method colors the cells of the heatmap based on the correlation values.

    • title = "Correlation Heatmap" sets the title of the heatmap to “Correlation Heatmap.”

When this code is executed, it will create an enhanced correlation heatmap that visually represents the correlations between the specified variables (Petal.Length, Petal.Width, Sepal.Length, Sepal.Width) in the iris dataset. The colors and intensity in the heatmap indicate the strength and direction of the correlations between these variables. This visualization is helpful for understanding the relationships between multiple variables in a dataset.

In ecological research, these visualization techniques aid in understanding the data, generating hypotheses, and communicating findings effectively. They are essential tools for any ecologist seeking to explore and analyze ecological datasets.

5.4 Summary Statistics

5.4.1 Summary Statistics Overview

Summary statistics are essential in ecological research for several reasons:

  1. Data Summarization: They provide a concise summary of large datasets, making it easier to grasp the dataset’s characteristics.

  2. Data Exploration: Summary statistics help ecologists understand the distribution, central tendency, and variability of ecological measurements.

  3. Comparison: They enable researchers to compare different datasets or subsets within a dataset.

5.4.2 Measures of Central Tendency

These measures describe the center or average of a dataset:

  1. Mean: The mean, also known as the average, is calculated by summing all values in a dataset and dividing by the number of values. It’s appropriate for normally distributed data.

  2. Median: The median is the middle value when data is sorted in ascending order. It’s robust to outliers and appropriate for skewed data.

  3. Mode: The mode is the most frequent value(s) in a dataset. It’s suitable for categorical or discrete data.

5.4.3 Measures of Variability

Measures of variability quantify the spread or dispersion of data:

  1. Variance: Variance measures how much each data point deviates from the mean. It’s calculated as the average of the squared differences between each data point and the mean.

  2. Standard Deviation: The standard deviation is the square root of the variance. It provides a more interpretable measure of dispersion in the same units as the data.

5.4.4 Quantiles and Percentiles

  1. Quantiles: Quantiles divide a dataset into equal portions. For instance, the median is the 50th percentile, dividing data into two equal halves. Quantiles can reveal data distribution and detect outliers.

  2. Percentiles: Percentiles are specific quantiles that indicate the relative standing of a value within a dataset. For example, the 25th percentile is the value below which 25% of the data falls.

The following code chunk below provides summary of all important descriptive stats outlined above.

# Load necessary packages
library(skimr)      # For data summary statistics
library(dplyr)      # For data manipulation
library(flextable)  # For creating formatted tables
library(elucidate)  # For quick data visualization

# Define formatting properties of tables using flextable
flextable::set_flextable_defaults(
  font.size = 12,
  # Set font size
  theme_fun = "theme_apa",
  # Apply APA-style theme
  font.family = "times",
  # Set font family
  digits = 3,
  # Number of decimal places
  font.color = "#FFFFFF"       # Font color (white)
)

# Display data properties for the CO2 dataset using skimr and create a flextable
CO2 %>% skimr::skim_without_charts() %>% flextable::flextable()

skim_type

skim_variable

n_missing

complete_rate

factor.ordered

factor.n_unique

factor.top_counts

numeric.mean

numeric.sd

numeric.p0

numeric.p25

numeric.p50

numeric.p75

numeric.p100

factor

Plant

0

1.00

TRUE

12

Qn1: 7, Qn2: 7, Qn3: 7, Qc1: 7

factor

Type

0

1.00

FALSE

2

Que: 42, Mis: 42

factor

Treatment

0

1.00

FALSE

2

non: 42, chi: 42

numeric

conc

0

1.00

435.00

295.92

95.00

175.00

350.00

675.00

1,000.00

numeric

uptake

0

1.00

27.21

10.81

7.70

17.90

28.30

37.12

45.50

# For only one variable (e.g., 'conc' column) in the CO2 dataset
CO2$conc %>% skimr::skim_without_charts() %>% flextable::flextable()

skim_type

skim_variable

n_missing

complete_rate

numeric.mean

numeric.sd

numeric.p0

numeric.p25

numeric.p50

numeric.p75

numeric.p100

numeric

data

0

1.00

435.00

295.92

95.00

175.00

350.00

675.00

1,000.00

# Group data by a factor variable ('Type' column) and create flextables for selected columns
CO2[, c(2, 4:5)] %>%
  dplyr::group_by(Type) %>%        # Group data by 'Type' column
  skimr::skim_without_charts() %>%                  # Calculate summary statistics
  flextable::qflextable()            # Create a flextable with APA-style formatting

skim_type

skim_variable

Type

n_missing

complete_rate

numeric.mean

numeric.sd

numeric.p0

numeric.p25

numeric.p50

numeric.p75

numeric.p100

numeric

conc

Quebec

0

1.00

435.00

297.72

95.00

175.00

350.00

675.00

1,000.00

numeric

conc

Mississippi

0

1.00

435.00

297.72

95.00

175.00

350.00

675.00

1,000.00

numeric

uptake

Quebec

0

1.00

33.54

9.67

9.30

30.33

37.15

40.15

45.50

numeric

uptake

Mississippi

0

1.00

20.88

7.82

7.70

13.87

19.30

28.05

35.50

# Quick plot/visual display of data for variables 'conc' and 'uptake'
CO2 %>% elucidate::plot_var_all(cols = c("conc", "uptake"))

R Code Explanation

  1. The code loads the necessary packages (skimr, dplyr), including elucidate for quick data visualization.

  2. Formatting properties for tables using flextable are defined. These properties include font size, theme, font family, number of decimal places, and font color, ensuring that all subsequent flextables adhere to these formatting settings.

  3. The CO2 dataset is summarized using skimr::skim_without_charts(), which provides summary statistics without charts. The result is then formatted into a table using flextable::flextable().

  4. To summarize a single variable (in this case, ‘conc’), the same process is repeated, but only the ‘conc’ column is selected for summary statistics.

  5. The script groups the data by the ‘Type’ column (renamed from ‘Plant’) and calculates summary statistics for the selected columns (columns 1, 4, and 5) within each group. The result is formatted into a table using flextable::qflextable(). This demonstrates how to perform group-wise summaries and format the results into an APA-style table.

  6. Finally, a quick visual display of the data for the ‘conc’ and ‘uptake’ variables is generated using elucidate::plot_var_all(), providing a convenient way to visualize these variables. Note that dashed lines on the density plots are theoretical normal distribution curves.

These codes enhance the data summarization and visualization capabilities for the CO2 dataset, making it easier to analyze and present the data.

5.4.5 Relevance in Ecology

  • In ecology, summarizing data helps researchers understand ecological patterns, such as species abundance or plant growth, and assess biodiversity in an ecosystem.

  • Measures of central tendency are used to describe typical values within ecological datasets. For instance, the mean body size of a species or the median population density.

  • Measures of variability are crucial for assessing the heterogeneity of ecological data, like the spread of species across habitats.

  • Quantiles and percentiles can help ecologists identify critical thresholds, such as the 90th percentile of pollution levels in a river, which can indicate environmental stress.

Overall, these summary statistics provide ecologists with a toolbox for effectively summarizing, analyzing, and interpreting ecological data. They are fundamental for gaining insights into ecological phenomena and supporting evidence-based decisions in conservation and environmental management.

5.5 Outliers in EDA

Outliers are data points that significantly differ from the majority of the data in a dataset. They are observations that are unusually high or low in value compared to the central tendency of the data. In ecological data analysis:

  • Outliers may represent rare events, such as extreme weather conditions or ecological disturbances.

  • They can indicate errors in data collection, data entry, or measurement.

  • Outliers can have a substantial impact on statistical analyses, potentially leading to biased results and incorrect conclusions.

  • Ecological processes are often complex, and outliers can be indicative of interesting and significant phenomena, such as invasive species or environmental stressors.

5.5.1 Outlier Detection Techniques

  • IQR (Interquartile Range) Method: The IQR is the range between the first quartile (Q1, 25th percentile) and the third quartile (Q3, 75th percentile) of the data. Outliers are defined as data points that fall below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR. This method is robust to extreme values and suitable for skewed distributions.

    # Detect outliers using the IQR method
Q1 <- quantile(iris$Sepal.Width, 0.25)
Q3 <- quantile(iris$Sepal.Width, 0.75)
IQR <- Q3 - Q1
lower_bound <- Q1 - 1.5 * IQR
upper_bound <- Q3 + 1.5 * IQR
iqr_outliers <-
  iris$Sepal.Width[iris$Sepal.Width < lower_bound |
                     iris$Sepal.Width > upper_bound]
print(iqr_outliers)
    ## [1] 4.4 4.1 4.2 2.0

    R Code Explanation

  • Q1 <- quantile(data, 0.25): This line calculates the first quartile (Q1), which represents the 25th percentile of the dataset data. The quantile() function is used to compute quartiles.

  • Q3 <- quantile(data, 0.75): This line calculates the third quartile (Q3), which represents the 75th percentile of the dataset.

  • IQR <- Q3 - Q1: The interquartile range (IQR) is calculated by subtracting Q1 from Q3. The IQR measures the spread of the middle 50% of the data.

  • lower_bound <- Q1 - 1.5 * IQR: The lower bound for potential outliers is computed by subtracting 1.5 times the IQR from Q1. Any data point below this lower bound is considered a potential outlier.

  • upper_bound <- Q3 + 1.5 * IQR: The upper bound for potential outliers is computed by adding 1.5 times the IQR to Q3. Any data point above this upper bound is considered a potential outlier.

  • outliers <- data[data < lower_bound | data > upper_bound]: In this line, potential outliers are identified. It selects data points where the data values are less than the lower bound or greater than the upper bound, as determined by the IQR method. These data points are stored in the variable outliers.

The IQR method is a robust technique for detecting outliers because it is less sensitive to extreme values compared to the Z-score method. It identifies potential outliers based on the spread of the central 50% of the data. In ecological data analysis, identifying and handling outliers is crucial for accurate statistical analyses and ecological interpretations.

  • Z-scores: A Z-score measures how many standard deviations a data point is from the mean. Values with Z-scores beyond a certain threshold (e.g., |Z| > 2) are considered outliers. This method is suitable for normally distributed data.
# Detect outliers using Z-scores
mean_val <- mean(iris$Sepal.Width)
std_dev <- sd(iris$Sepal.Width)
Z_scores <- (iris$Sepal.Width - mean_val) / std_dev
z_outliers <- iris$Sepal.Width[abs(Z_scores) > 2]
print(z_outliers)
## [1] 4.0 4.4 4.1 4.2 2.0

R Code Explanation

  • mean_val <- mean(data): This line calculates the mean (average) value of the dataset data. The mean() function computes the arithmetic mean of a numeric vector.

  • std_dev <- sd(data): This line calculates the standard deviation of the dataset data. The sd() function calculates the sample standard deviation.

  • Z_scores <- (data - mean_val) / std_dev: Z-scores are calculated for each data point in the dataset. Z-scores indicate how many standard deviations a data point is away from the mean. A Z-score of 2 (or -2) is often used as a threshold to identify potential outliers.

  • outliers <- data[abs(Z_scores) > 2]: In this line, potential outliers are identified. It selects data points where the absolute value of the Z-score (abs(Z_scores)) is greater than 2. These data points are considered potential outliers and are stored in the variable outliers.

The Z-score method is a common technique for detecting outliers. By calculating the Z-scores for each data point and comparing them to a threshold (in this case, 2), you can identify data points that deviate significantly from the mean. These identified data points are often flagged as potential outliers.

In ecological data analysis, identifying outliers is essential as they can skew statistical analyses and affect the accuracy of ecological interpretations.

5.5.2 Visual Inspection of Box Plots

Box plots provide a visual way to detect outliers by displaying the distribution of data and highlighting potential outliers. In a box plot:

  • Data points below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR are typically marked as individual points, allowing you to identify them easily.

  • Box plots provide a quick overview of the spread of data and help identify skewness or asymmetry in the distribution.

# Create a box plot to visualize potential outliers
boxplot(iris$Sepal.Width, main = "Box Plot with Outliers")

R Code Explanation

  • boxplot(data, main = "Box Plot with Outliers"): This line of code generates a box plot of the data stored in the variable data. The boxplot() function is used for creating box plots in R.

  • data: This should be replaced with the actual name of the dataset you want to visualize for potential outliers.

  • main = "Box Plot with Outliers": This part of the code specifies the title or main title of the box plot. In this case, the title is set to “Box Plot with Outliers” to provide context for the plot.

The resulting box plot will display the distribution of the data and highlight any potential outliers. In a box plot:

  • The box represents the interquartile range (IQR), which contains the middle 50% of the data.

  • The line inside the box represents the median (the middle value when the data is sorted).

  • “Whiskers” extend from the box to the minimum and maximum values within a defined range (usually 1.5 times the IQR).

  • Data points beyond the whiskers are considered potential outliers and are typically displayed as individual points.

This visualization allows you to quickly identify any data points that fall outside the “whiskers,” indicating that they may be outliers. It provides a visual summary of the data’s spread and helps you assess the distribution’s symmetry and skewness.

Box plots are valuable for identifying and visualizing potential outliers, which can have a significant impact on the results of statistical analyses and ecological interpretations.

Visual inspection of box plots is an intuitive way to identify outliers, especially when dealing with smaller datasets. It provides a qualitative assessment of data distribution and potential anomalies.

In ecological data analysis, detecting outliers is critical to ensure the integrity and accuracy of analyses. Addressing outliers appropriately, whether by excluding them or using robust statistical methods, is essential to avoid bias and ensure the validity of ecological research findings.

5.6 Conclusion

Exploratory Data Analysis (EDA) is a fundamental step in ecological research, providing essential insights into your datasets:

  1. Importance of EDA: EDA is the process of visually and statistically exploring your data to understand its characteristics. It helps uncover patterns, relationships, and potential outliers in your ecological datasets.

  2. Data Visualization: EDA relies heavily on data visualization techniques. You learned how to create various types of plots, including histograms, density plots, box plots, scatter plots, bar charts, and correlation heatmaps.

  3. Univariate Visualization: You can explore single variables using histograms, density plots, and box plots. These visualizations provide a sense of the data’s distribution, central tendency, and variability.

  4. Bivariate Visualization: To understand relationships between two variables, scatter plots, bar charts, and correlation plots are used. These visualizations help identify patterns, associations, and potential dependencies.

  5. Multivariate Visualization: Exploring interactions among multiple variables is crucial in ecological research. Techniques like heatmaps, stacked bar charts, and parallel coordinate plots reveal complex relationships and dependencies within ecological datasets.

  6. Summary Statistics: Beyond visualization, summary statistics like mean, median, mode, variance, and standard deviation provide numerical insights into the central tendency and variability of your data.

  7. Outlier Detection: Identifying and handling outliers is an integral part of EDA. Techniques like the IQR method, Z-scores, and visual inspection of box plots help detect and address potential outliers.

In conclusion, EDA is a foundational step in ecological research. By conducting thorough exploratory data analysis, you gain a deep understanding of your ecological datasets. This knowledge empowers you to make informed decisions about subsequent analyses, hypothesis testing, and research directions. EDA is a powerful tool for uncovering the hidden stories within your ecological data.

6 Chapter 4: Statistical Tests

6.1 Introduction

Chapter 4 delves into the core of statistical data analysis for ecological research. You will gain a comprehensive understanding of statistical hypothesis testing and learn to perform a variety of tests commonly used in ecology. By the end of this chapter, you will have:

  • Acquired knowledge of fundamental statistical concepts.

  • Explored various statistical tests relevant to ecological research.

  • Gained hands-on experience in conducting these tests using R and Jamovi.

6.2 Hypothesis Testing Fundamentals

In ecological research, hypothesis testing plays a crucial role in making data-driven decisions and drawing valid conclusions from data. It allows researchers to systematically evaluate whether there is enough evidence to support a particular claim or hypothesis about ecological phenomena. Hypothesis testing helps distinguish between random variation in data and meaningful patterns or effects.

6.2.1 Null hypothesis (H0) and alternative hypothesis (Ha)

  • Null Hypothesis (H0): The null hypothesis is a statement that suggests there is no significant effect, relationship, or difference between groups or variables in the population being studied. It serves as a default assumption or starting point for hypothesis testing.

  • Alternative Hypothesis (Ha): The alternative hypothesis is a statement that contradicts the null hypothesis. It suggests that there is a significant effect, relationship, or difference in the population. Researchers typically design experiments or analyses with the hope of finding evidence to support the alternative hypothesis.

6.2.2 Significance Level (Alpha)

  • The significance level, denoted as alpha (α), is a critical parameter in hypothesis testing. It represents the threshold for determining statistical significance. In other words, it sets the standard for how strong the evidence must be to reject the null hypothesis.

  • Commonly used alpha values include 0.05 (5%) and 0.01 (1%). A significance level of 0.05 means that the researcher is willing to accept a 5% chance of making a Type I error (rejecting the null hypothesis when it’s true). A lower alpha (e.g., 0.01) requires stronger evidence to reject the null hypothesis but increases the risk of Type II errors (failing to reject the null hypothesis when it’s false). The choice of alpha depends on the research question, the consequences of Type I and Type II errors, and prevailing scientific standards.

Understanding these fundamental concepts of hypothesis testing is essential for conducting meaningful ecological research and making valid inferences from data. Researchers design experiments, collect data, and perform statistical tests with the aim of either supporting the alternative hypothesis or failing to reject the null hypothesis, based on the evidence provided by the data. The significance level alpha serves as a critical tool for controlling the balance between making Type I and Type II errors, ensuring that research findings are robust and reliable.

6.3 Parametric vs. Non-Parametric Tests:

6.3.1 Distinguishing Parametric and Non-Parametric Tests

  • Parametric Tests: Parametric tests are statistical tests that make specific assumptions about the population distribution, such as normality and homogeneity of variances. These tests rely on the estimation of population parameters (e.g., means and variances) and often provide more statistical power when the assumptions are met.

  • Non-Parametric Tests: Non-parametric tests are statistical tests that do not rely on assumptions about the population distribution. They are distribution-free tests that use ranking and order statistics to make inferences about the population. Non-parametric tests are robust to violations of distributional assumptions.

6.3.2 When to use each type of test based on data characteristics

  • Parametric tests are appropriate when data meet the assumptions of normality and homogeneity of variances. They are more powerful than non-parametric tests when these assumptions are met.

  • Non-parametric tests are suitable when data do not meet the assumptions of normality and homogeneity of variances or when dealing with ordinal or categorical data. They are also preferred when researchers want to make minimal distributional assumptions.

6.3.3 How to use parametric tests like t-tests, ANOVA, and linear regression

  • T-Tests: T-tests are used to compare the means of two groups or conditions. For example, in ecology, a t-test can be used to compare the mean tree height between two different treatment groups.

  • ANOVA (Analysis of Variance): ANOVA is used to compare the means of three or more groups or conditions. In ecology, it can be applied to compare the mean biomass across multiple vegetation types.

  • Linear Regression: Linear regression is used to model the relationship between a dependent variable and one or more independent variables. Ecological examples include modeling the relationship between temperature and species diversity.

6.3.4 How to use non-parametric tests like Mann-Whitney U test and Kruskal-Wallis test

  • Mann-Whitney U Test: The Mann-Whitney U test compares the distributions of two independent groups when the assumptions for a t-test are not met. For example, it can be used to compare the abundance of a species in two different habitats.

  • Kruskal-Wallis Test: The Kruskal-Wallis test extends the Mann-Whitney U test to three or more independent groups. It is used when comparing medians across multiple groups, such as testing the effect of different soil types on plant growth.

Understanding when to use parametric and non-parametric tests is crucial for ecological research. Parametric tests are powerful when assumptions are met, while non-parametric tests provide robust alternatives when assumptions are violated or when dealing with non-normally distributed data. The choice between these two types of tests should be based on the nature of the data and the specific research question at hand.

6.4 Performing Statistical Tests in R and Jamovi

6.4.1 Overview of R and Jamovi for Statistical Tests

  • R: R is a versatile and powerful statistical programming language. It offers a wide range of packages and libraries specifically tailored for ecological data analysis. R provides the flexibility to perform basic to advanced statistical tests, hypothesis testing, regression analysis, multivariate analysis, spatial analysis, and more. Its extensive graphical capabilities also enable the creation of informative data visualizations, which are crucial for ecological research.

  • Jamovi: Jamovi is a user-friendly statistical software that simplifies data analysis. It is particularly suitable for beginners in ecological research due to its intuitive graphical interface and point-and-click functionality. Jamovi seamlessly integrates with R, allowing users to transition from simple analyses in Jamovi to more complex statistical tests in R as they gain proficiency. Jamovi’s ecosystem includes a range of statistical tests commonly used in ecological research.

6.4.2 Benefits of using these tools for data analysis

  1. Versatility: Both R and Jamovi offer a wide array of statistical tests commonly used in ecological research. Researchers can perform t-tests, ANOVA, regression analysis, non-parametric tests, and advanced multivariate analyses using these tools.

  2. Flexibility: R, in particular, provides unlimited flexibility. Users can customize analyses, create bespoke statistical models, and develop complex ecological workflows to suit their research needs.

  3. Visualization: Both R and Jamovi excel in data visualization. Researchers can create publication-quality graphs, plots, and charts to present their ecological findings effectively.

  4. Integration: Jamovi’s integration with R is a valuable feature. Users can start with simple analyses in Jamovi and gradually transition to more advanced analyses in R as their skills grow.

  5. Community Support: R benefits from a large and active user community. Researchers can find extensive resources, tutorials, and forums to seek help and share knowledge. Jamovi also has a growing community and offers user support.

  6. Open Source: Both R and Jamovi are open-source software, making them accessible and cost-effective tools for ecological research.

  7. Reproducibility: Using R or Jamovi for data analysis enhances the reproducibility of ecological research. Researchers can document their analyses, share code, and ensure transparency in their work.

  8. Teaching and Learning: Jamovi’s user-friendly interface makes it an excellent tool for teaching ecological data analysis to students and beginners. R, with its extensive capabilities, serves as a powerful teaching tool for advanced statistical concepts.

In summary, R and Jamovi offer a robust and accessible environment for ecological data analysis. They empower researchers, from beginners to experts, to conduct a wide range of statistical tests, explore data visually, and enhance the rigor and reproducibility of ecological research.

6.4.3 Step-by-Step Test Procedures

6.4.3.1 R: Performing t-Test, Mann-Whitney U test, Anova and Kruskal-Wallis tests

  1. Set Up Your Environment and perform t-test

  2. First do normality test to decide whether to use a parametric or non-parametric test.

  • Normality test
# Load necessary libraries (if not already loaded)
library(tidyverse)  # Loads the tidyverse package for data manipulation and visualization.
library(janitor)    # Loads the janitor package for data cleaning.
library(report)     #  Load the report package, for generating summary reports.

# Load the InsectSprays dataset
data("InsectSprays")

# Perform the Shapiro-Wilk normality test on the 'count' variable
shapiro_test_result <- stats::shapiro.test(InsectSprays$count)

# View the normality test result
print(shapiro_test_result)
## 
##  Shapiro-Wilk normality test
## 
## data:  InsectSprays$count
## W = 0.9216, p-value = 0.0002525
# create a function to interpret the result
if (shapiro_test_result$p.value < 0.05) {
  cat(
    "The data is not normally distributed (p < 0.05). Select a non-parametric counterpart test.\n"
  )
} else {
  cat("The data is normally distributed (p >= 0.05). Proceed with parametric test.\n")
}
## The data is not normally distributed (p < 0.05). Select a non-parametric counterpart test.

R Code Explanation

This code loads necessary libraries, loads the InsectSprays dataset, performs the Shapiro-Wilk normality test on the count variable, and prints the test result. The interpretation is provided using a function based on the p-value, indicating whether the data is normally distributed or not, and suggesting whether to proceed with a parametric or non-parametric test accordingly.

  • Mann-Whitney U Test (non-parametric test)
# Load necessary libraries (if not already loaded)
library(tidyverse)  # Loads the tidyverse package for data manipulation and visualization.
library(janitor)    # Loads the janitor package for data cleaning.
library(report)     #  Load the report package, for generating summary reports.

# Use the InsectSprays data to test for the effectiveness of Insect Sprays.The dataset contains counts of insects in agricultural experimental units treated with different insecticides.
data("InsectSprays")

# Subset the dataset to use only two types of insecticides (spray A and spray B). The dplyr::filter() function is used to filter rows where spray is either "A" or "B".
insectides <- InsectSprays %>% dplyr::filter(spray %in% c("A", "B"))
# Perform the Mann-Whitney U Test on the 'insectides' dataset
mann_whitney_result <-
  stats::wilcox.test(count ~ spray, data = insectides, alternative = "two.sided")

# View the Mann-Whitney U Test result
print(mann_whitney_result)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  count by spray
## W = 62, p-value = 0.5812
## alternative hypothesis: true location shift is not equal to 0
# create a function to interpret the result
if (mann_whitney_result$p.value < 0.05) {
  cat("There is a significant difference between spray 'A' and spray 'B' (p < 0.05).\n")
} else {
  cat("There is no significant difference between spray 'A' and spray 'B' (p >= 0.05).\n")
}
## There is no significant difference between spray 'A' and spray 'B' (p >= 0.05).

R Code Explanation

  1. Loading Necessary Libraries: The code begins by loading several R packages using the library() function. Each package serves a specific purpose in the analysis:

    • tidyverse: This package is loaded for data manipulation and visualization. The “tidyverse” collection includes a set of packages that make data analysis and visualization more efficient and consistent.

    • janitor: The “janitor” package is loaded for data cleaning tasks. It provides functions for cleaning and tidying data, which is an essential step in data analysis.

    • report: The “report” package is loaded to facilitate the generation of summary reports based on statistical analysis results. It automates the report creation process.

  2. Loading the InsectSprays Dataset: The code loads the “InsectSprays” dataset using the data() function. This dataset contains information about counts of insects in agricultural experimental units treated with different insecticides. It’s a common dataset used for statistical testing and analysis.

  3. Subsetting the Dataset: The insectides variable is created by subsetting the original dataset. It selects only the rows where the “spray” column has values “A” or “B.” This subset of data will be used for the Mann-Whitney U Test, focusing on comparing the effectiveness of these two insecticide sprays.

  4. Performing the Mann-Whitney U Test: The Mann-Whitney U Test is conducted using the wilcox.test() function. It assesses whether there is a significant difference in the distribution of insect counts between spray “A” and spray “B.” The count ~ spray formula specifies that the “count” variable is being compared across the different “spray” groups.

  5. Viewing the Test Result: The result of the Mann-Whitney U Test is printed to the console using the print() function. This result includes statistics such as the U statistic and the p-value, which are crucial for interpreting the test outcome.

  6. Interpreting the Result: A conditional statement is used to interpret the test result. If the p-value is less than 0.05 (typically chosen as the significance level), it suggests that there is a significant difference between spray “A” and spray “B” regarding their effectiveness in controlling insects. If the p-value is greater than or equal to 0.05, it suggests that there is no significant difference between the two sprays.

In summary, this code demonstrates how to perform and interpret a Mann-Whitney U Test using R. It focuses on comparing the effectiveness of two insecticide sprays (“A” and “B”) in controlling insect populations based on count data. The “report” package is used to facilitate report generation, which can be helpful for documenting and communicating the results of statistical tests.

  • t-Test (parametric test; assuming normality test above is p >= 0.05)
# Load necessary libraries (if not already loaded)
library(tidyverse)  # Loads the tidyverse package for data manipulation and visualization.
library(janitor)    # Loads the janitor package for data cleaning.
library(report)     #  Load the report package, for generating summary reports.

# Use the InsectSprays data to test for the effectiveness of Insect Sprays.The dataset contains counts of insects in agricultural experimental units treated with different insecticides.
data("InsectSprays")

# Subset the dataset to use only two types of insecticides (spray A and spray B). The dplyr::filter() function is used to filter rows where spray is either "A" or "B".
insectides <- InsectSprays %>% dplyr::filter(spray %in% c("A", "B"))

# Assuming you want to compare two groups (spray A and spray B).
# Perform a t-Test for independent samples using the stats::t.test() function.
# The formula count ~ spray specifies that you want to compare the 'count' variable across different 'spray' groups.
# 'data = insectides' specifies the dataset to use.
t_test_result <- stats::t.test(count ~ spray, data = insectides)

# View the t-test result using the print() function.
t_test_result %>% print()
## 
##  Welch Two Sample t-test
## 
## data:  count by spray
## t = -0.45352, df = 21.784, p-value = 0.6547
## alternative hypothesis: true difference in means between group A and group B is not equal to 0
## 95 percent confidence interval:
##  -4.646182  2.979515
## sample estimates:
## mean in group A mean in group B 
##        14.50000        15.33333
# autogenerate a report. Ingnore the warning.
t_test_result %>% report::report()
## Effect sizes were labelled following Cohen's (1988) recommendations.
## 
## The Welch Two Sample t-test testing the difference of count by spray (mean in
## group A = 14.50, mean in group B = 15.33) suggests that the effect is negative,
## statistically not significant, and very small (difference = -0.83, 95% CI
## [-4.65, 2.98], t(21.78) = -0.45, p = 0.655; Cohen's d = -0.19, 95% CI [-1.03,
## 0.65])

R Code Explanation

  1. Libraries are loaded to make the necessary functions available for data manipulation (tidyverse) and cleaning (janitor).

  2. The InsectSprays dataset is loaded, which contains information about the effectiveness of various insect sprays in controlling insect populations.

  3. The dataset is subsetted to include only two types of insecticides, “A” and “B,” using the dplyr::filter() function.

  4. The t-test is performed using stats::t.test(). It compares the ‘count’ of insects between the two groups defined by ‘spray’ (A and B).

  5. The t-test result is stored in the variable ‘t_test_result.’

  6. The t-test result is printed to the console using the print() function.

  7. Finally, the script generates an automatic report using the report::report() function, providing a summary of the t-test results.

This script helps you assess whether there is a significant difference in the effectiveness of insect sprays A and B in controlling insect populations. The t-test compares the means of the ‘count’ variable between the two groups and provides information about the statistical significance of any observed differences.

Check the p-value in the t-test result. If p < 0.05 (assuming a significance level of 0.05), you can reject the null hypothesis (H0) and conclude that there is a significant difference between the groups.

Below are other tests conducted in R.

One-Way ANOVA (parametric)

# Load necessary libraries (if not already loaded)
library(tidyverse)

# Load the InsectSprays dataset
data("InsectSprays")

# Subset the dataset to use only two types of insecticides (spray A and spray B)
insecticides <-
  InsectSprays %>% dplyr::filter(spray %in% c("A", "B"))

# Perform a one-way ANOVA
anova_result <- stats::aov(count ~ spray, data = insecticides)

# View the ANOVA result
summary(anova_result)
##             Df Sum Sq Mean Sq F value Pr(>F)
## spray        1    4.2   4.167   0.206  0.655
## Residuals   22  445.7  20.258

Two-Way ANOVA (parametric)

# Perform a two-way ANOVA
two_way_anova_result <-
  stats::aov(count ~ spray, data = InsectSprays)

# View the two-way ANOVA result
summary(two_way_anova_result)
##             Df Sum Sq Mean Sq F value Pr(>F)    
## spray        5   2669   533.8    34.7 <2e-16 ***
## Residuals   66   1015    15.4                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Kruskal-Wallis Test (non-parametric)

# Load necessary libraries (if not already loaded)
library(tidyverse)

# Perform a Kruskal-Wallis test
kruskal_wallis_result <-
  stats::kruskal.test(count ~ spray, data = InsectSprays)

# View the Kruskal-Wallis test result
kruskal_wallis_result
## 
##  Kruskal-Wallis rank sum test
## 
## data:  count by spray
## Kruskal-Wallis chi-squared = 54.691, df = 5, p-value = 1.511e-10

Post-Hoc Pairwise Comparison Test

To perform a post hoc test with Bonferroni correction using the Agricolae R package on the InsectSprays dataset, you can follow these steps:

  1. Install and load the Agricolae package (if not already installed).

  2. Perform a Kruskal-Wallis test on the dataset.

  3. Conduct a post hoc test with Bonferroni correction to compare groups.

Here’s the R code to achieve this:

# Install and load the required packages
# We use 'pacman' to install and load packages in a single step.
# If not already installed, 'pacman' will install the packages.
# 'agricolae' for conducting Kruskal-Wallis tests and post hoc analysis.
# 'install = TRUE' specifies to install the packages if not present.
# 'update = FALSE' prevents updating existing packages.
pacman::p_load(agricolae, install = TRUE, update = FALSE)

# Load the InsectSprays dataset
# The 'data()' function loads the InsectSprays dataset, which contains insect count data.
data("InsectSprays")

# Perform Kruskal-Wallis test without grouping
# 'agricolae::kruskal()' conducts the Kruskal-Wallis test.
# We specify the 'count' variable as the dependent variable and 'spray' as the independent variable.
# 'group = FALSE' indicates that we don't want to group the results.
# 'p.adj = "bon"' specifies Bonferroni correction for post hoc tests.
comparison_stats <- with(InsectSprays,
                         agricolae::kruskal(count, spray,
                                            group = FALSE,
                                            p.adj = "bon"))

# Display selected statistical results
# We extract specific results from the 'comparison_stats' object.
# In this case, we're interested in columns 1, 2, and 4.
comparison_stats[c(1:2, 4)]
## $statistics
##      Chisq Df      p.chisq  t.value      MSD
##   54.69134  5 1.510845e-10 3.045792 12.91015
## 
## $parameters
##             test  p.ajusted name.t ntr alpha
##   Kruskal-Wallis bonferroni  spray   6  0.05
## 
## $comparison
##        Difference pvalue Signif.        LCL        UCL
## A - B  -2.6666667 1.0000         -15.576816  10.243483
## A - C  40.7083333 0.0000     ***  27.798184  53.618483
## A - D  26.5833333 0.0000     ***  13.673184  39.493483
## A - E  32.8333333 0.0000     ***  19.923184  45.743483
## A - F  -3.4583333 1.0000         -16.368483   9.451816
## B - C  43.3750000 0.0000     ***  30.464851  56.285149
## B - D  29.2500000 0.0000     ***  16.339851  42.160149
## B - E  35.5000000 0.0000     ***  22.589851  48.410149
## B - F  -0.7916667 1.0000         -13.701816  12.118483
## C - D -14.1250000 0.0212       * -27.035149  -1.214851
## C - E  -7.8750000 1.0000         -20.785149   5.035149
## C - F -44.1666667 0.0000     *** -57.076816 -31.256517
## D - E   6.2500000 1.0000          -6.660149  19.160149
## D - F -30.0416667 0.0000     *** -42.951816 -17.131517
## E - F -36.2916667 0.0000     *** -49.201816 -23.381517
# Perform Kruskal-Wallis test with grouping
# This time, we set 'group = TRUE' to group the results for plotting.
comparison_grp <- with(InsectSprays,
                       agricolae::kruskal(count, spray,
                                          group = TRUE,
                                          p.adj = "bon"))

# Plot group comparison
# 'agricolae::plot.group()' is used to create a bar chart of group comparisons.
# 'variation = "SE"' specifies to display standard errors.
# 'decreasing = TRUE' orders the bars in descending order of means.
# 'main = "Insecticide Sprays"' sets the chart's title.
agricolae::plot.group(
  comparison_grp,
  variation = "SD",
  decreasing = TRUE,
  main = "Comparing Effect of \nInsecticide Sprays",
  xlab = "Sprays",
  ylab = "Insect Count"
)

R Code Explanation

  • The code begins by installing and loading the necessary R packages using the ‘pacman’ package manager.

  • The ‘InsectSprays’ dataset is loaded using the ‘data()’ function. This dataset contains insect count data.

  • Two Kruskal-Wallis tests are performed, one without grouping and one with grouping. The ‘agricolae::kruskal()’ function is used for this purpose.

  • Bonferroni correction (‘p.adj = "bon"’) is applied to adjust p-values in post hoc tests.

  • Selected statistical results are displayed for the first Kruskal-Wallis test.

  • A bar chart of group comparisons is created for the second Kruskal-Wallis test using ‘agricolae::plot.group()’. This chart displays standard errors, orders bars by decreasing means, and sets the title.

Overall, this code demonstrates the use of the ‘agricolae’ package for Kruskal-Wallis tests and post hoc analysis, along with visualizing group comparisons.

6.4.3.2 Jamovi: Performing t-Test, Mann-Whitney U test, Anova and Kruskal-Wallis tests

Step 1: Set Up Your Environment

Open Jamovi and load your ecological dataset. We’ll use the same dataset “InsectSprays”. First in R, save this data as a flat csv file to your data directory. Here the dataset in called “insecticide”.

# Load the readr package
# Load the readr package
library(readr)
# Load the here package for managing file paths
library(here)


# Write the InsectSprays dataset to a CSV file

# Specify the dataset to be written (InsectSprays)
# Specify the file path where the CSV file will be saved (./docs/data/insecticide.csv)
# Specify that column names should be included in the CSV file (col_names = TRUE)
readr::write_csv(
  InsectSprays,
  # Dataset to be written
  file = here::here("docs", "data", "insecticide.csv"),
  # File path and name
  col_names = TRUE,
  # Include column names in the CSV file
  append = FALSE                   # Don't append to an existing file, create a new one
)

R Code Explanation

  • This section of the code is responsible for writing the InsectSprays dataset to a CSV file.

  • readr::write_csv() is used to write the CSV file. Here’s what each argument does:

    • InsectSprays: The first argument is the dataset you want to write to the CSV file, in this case, it’s the InsectSprays dataset.

    • file: This argument specifies the file path and name for the CSV file. The here::here() function is used to create a file path that is relative to the project’s root directory. It specifies that the file should be saved in the “docs/data” directory with the name “insecticide.csv.”

    • col_names: This argument specifies whether column names should be included in the CSV file. Setting it to TRUE means that the first row of the CSV file will contain the column names.

  • append = FALSE ensures that if a file with the same name already exists at the specified path, it won’t be appended to. Instead, a new file will be created, potentially overwriting the existing one.

In summary, this code loads the necessary packages, specifies the dataset to be written, defines the file path and name, specifies that column names should be included in the CSV file, and ensures that a new CSV file is created at the specified location.

Step 2: Perform the t-Test, Mann-Whitney, One-Way and Two-Way Anova; and Kruskal-Wallis tests.

  1. Open the file in Jamovi.

    import insecticide data

  2. Remove unnecessary columns/ variables

    remove unwanted cols

  3. Append new columns to the original dataset. Note that we would need these variables for the t-test, mann-whitney and one-way anova tests. These tests require the data to have a grouping variable with 2 levels. Other variables with > 2 variables can used in a two-way anova etc.

  4. Add two new columns and named as “count2” and “spray2”. change their measure types for count2 as “continuous” and spray2 as “nominal”. Measure/ data types should be the same as the original variables (i.e., “count” and “spray”).

    add columns and change measure types.

  5. Click on “Analyses” in the top menu.

  6. Select “T-Tests”.

  7. Choose “Independent Samples T-Test” if comparing two groups or “One Sample T-Test” if comparing against a fixed value.

  8. Drag and drop your ecological variable of interest into the “Test Variables” box.

  9. Drag and drop your grouping variable into the “Grouping Variable” box (for independent samples t-test).

    jmv t-test

  10. Customize options and click “OK.”

  11. Now perform the one-way anova test.

    jmv 1-way aov

  12. Selected appropriate statistics to appear in the results.

    jmv 1-way aov results

  13. Do the same for the two-way anova. Use the original variables with > 2 spray levels. You can perform a post-hoc comparison if anova test is significant (p < 0.05). Note that our data as previously diagnosed does not conform to the normality assumption hence a non-parametric counterpart test in advisable.

    jmv 2-way aov results

  14. Next, perform Kruskal-Wallis test. Notice normality test is p < 0.05 from the two-way anova test. Notice p < 0.05 so a further pairwise comparison is appropriate.

    jmv kw test results

Step 3: Interpret the Results

  • Examine the output for the t-test. Similar to R, look for the p-value. If p < 0.05 (assuming a significance level of 0.05), you can reject the null hypothesis (H0) and conclude that there is a significant difference between the groups.

6.5 Interpreting Test Results:

Interpreting the results of statistical tests is a critical aspect of ecological research. Here’s a general guideline on how to interpret the results, with a focus on understanding p-values and effect sizes:

  1. Understand the Null Hypothesis (H0) and Alternative Hypothesis (Ha): Before interpreting the results, it’s essential to recall the null hypothesis (H0) and alternative hypothesis (Ha) that you formulated for your test. The null hypothesis typically represents the absence of an effect or relationship, while the alternative hypothesis states the expected outcome.

  2. Examine the Test Statistic: Most statistical tests generate a test statistic (e.g., t-statistic, F-statistic, chi-square statistic) that quantifies the difference or relationship observed in the data. Larger test statistics often indicate stronger evidence against the null hypothesis.

  3. Check the p-value: The p-value measures the strength of evidence against the null hypothesis. It represents the probability of obtaining results as extreme as, or more extreme than, the observed results if the null hypothesis is true. A small p-value (typically less than the chosen significance level, alpha) suggests strong evidence against the null hypothesis. Conversely, a large p-value suggests weak evidence against it.

    • Interpretation of p-values:

      • p < alpha (e.g., p < 0.05): Strong evidence against H0; you may reject the null hypothesis.

      • p >= alpha: Weak evidence against H0; you fail to reject the null hypothesis.

  4. Consider the Effect Size: While p-values tell you whether there is a significant difference or relationship, effect sizes provide information about the practical or clinical significance of the result. Effect sizes quantify the strength or magnitude of the observed effect. In ecological research, understanding the biological or ecological significance of an effect is often more important than its statistical significance.

    • Common effect size measures: Cohen’s d (for t-tests), eta-squared (for ANOVA), correlation coefficients, odds ratios (for logistic regression), etc.

  5. Look at Confidence Intervals: Confidence intervals provide a range of values within which the true population parameter (e.g., mean, proportion) is likely to fall. They complement p-values and offer additional insights into the precision of your estimates.

  6. Consider Ecological Relevance: In ecological research, it’s crucial to consider whether the results have practical significance. Statistical significance may not always translate to ecological significance. Evaluate the results in the context of your research question and the potential impact on the ecosystem or species you are studying.

  7. Replication and Consistency: Consider whether the results are consistent with previous research or if they need to be replicated in other studies or under different conditions to strengthen their validity.

  8. Beware of Multiple Comparisons: If you are conducting multiple tests on the same dataset, be cautious about the issue of multiple comparisons. Adjusting alpha (e.g., Bonferroni correction) can help control the familywise error rate.

  9. Consult Experts: If you are unsure about the interpretation of your results, consider seeking guidance from statistical or ecological experts. Collaborating with colleagues who have expertise in the field can enhance the quality of your interpretation.

This is a general overview of performing a t-test, mann-whitney u test, anova and kruskall-wallis tests in both R and Jamovi. The specific steps may vary depending on your dataset and research question. In ecological research, it’s not only important to detect statistically significant results but also to understand their ecological implications. A strong understanding of p-values, effect sizes, and their ecological relevance will contribute to more meaningful and robust ecological research outcomes.

6.6 Conclusion:

Chapter 4 provides comprehensive insights into statistical hypothesis testing, which is a fundamental aspect of ecological research.

  • You have learned about the significance of hypothesis testing in ecological research, where it helps you make data-driven decisions and draw conclusions about ecological phenomena.

  • Key terms like null hypothesis (H0), alternative hypothesis (Ha), and significance level (alpha) have been defined and their roles in hypothesis testing explained.

  • You now understand the distinction between parametric and non-parametric tests, as well as when to use each type based on data characteristics.

  • Parametric tests such as t-tests, ANOVA, and linear regression have been introduced, along with practical ecological examples for each.

  • Non-parametric tests like Mann-Whitney U and Kruskal-Wallis have also been explained, along with ecological examples.

  • You’ve gained practical skills through step-by-step instructions for performing these tests in both R and Jamovi.

  • The importance of interpreting results, understanding p-values and effect sizes, and considering ecological relevance has been emphasized.

Overall, Chapter 4 equips you with a strong foundation in statistical hypothesis testing, empowering you to conduct a wide range of tests essential for ecological data analysis and make informed ecological conclusions.

7 Chapter 5: Regression Analysis

7.1 Introduction

Chapter 5 is a deep dive into regression analysis, a powerful tool for modeling ecological relationships. In this chapter, you will learn about two essential types of regression: linear and logistic. By the end of this chapter, you will have:

  • A solid understanding of regression analysis and its relevance in ecological research.

  • Proficiency in performing linear and logistic regression in both R and Jamovi.

  • The ability to interpret regression outputs and draw meaningful ecological insights.

7.2 Understanding Regression Analysis

Regression analysis is a powerful statistical method used to model relationships between variables. It helps us understand how one or more independent variables are related to a dependent variable and how changes in the independent variables impact the dependent variable. In ecological research, regression analysis plays a crucial role in modeling ecological relationships, making predictions, and understanding the impact of environmental factors on biological phenomena.

Key Concepts:

  1. Dependent Variable (Response Variable): This is the variable we want to predict or explain. In ecological research, it could be the population of a species, the growth rate of a plant, or any other measurable ecological outcome.

  2. Independent Variables (Predictors or Explanatory Variables): These are the variables that we believe influence or explain changes in the dependent variable. Independent variables can be continuous (e.g., temperature, rainfall) or categorical (e.g., habitat type, presence/absence of a predator).

  3. Regression Equation: The mathematical formula that represents the relationship between the dependent and independent variables. It allows us to make predictions based on the values of the independent variables.

  4. Types of Regression: There are different types of regression analysis, including linear regression (for continuous dependent variables), logistic regression (for binary outcomes), and more complex forms like polynomial regression and mixed-effects models.

Applications in Ecological Research

  1. Species-Habitat Relationships: Ecologists often use regression analysis to model how the abundance or presence of a species is related to habitat variables such as vegetation type, temperature, or elevation.

  2. Climate Change Impact: Regression models can help assess the impact of climate change variables (e.g., temperature, precipitation) on ecological systems, predicting how ecosystems may respond to future climate scenarios.

  3. Population Dynamics: Ecological researchers use regression to model population growth, decline, or other changes over time. For example, how does temperature affect the growth rate of a plant species?

  4. Community Ecology: Regression can be applied to understand the relationships between species richness, diversity, and various environmental factors, shedding light on the mechanisms driving community structure.

  5. Ecosystem Functioning: Researchers explore how changes in ecological variables (e.g., nutrient availability) impact ecosystem functions (e.g., carbon cycling) using regression modeling.

Regression analysis is a fundamental tool in ecological research that allows researchers to quantify and understand the relationships between ecological variables. It helps in making predictions, testing hypotheses, and gaining insights into the complex dynamics of ecological systems.

7.3 Linear Regression

Definition: Linear regression is a statistical method used to model the relationship between a dependent variable (DV) and one or more independent variables (IVs) by fitting a linear equation to observed data. It assumes a linear relationship between the IVs and the DV, where changes in the IVs lead to a proportional change in the DV.

7.3.1 Applications in Ecological Research

  1. Species Abundance: Linear regression can be used to understand how environmental factors like temperature, precipitation, or habitat type influence the abundance of a particular species.

  2. Growth Rates: Ecologists often use linear regression to model the growth rates of plants or animal populations as a function of variables like temperature or nutrient availability.

  3. Biodiversity: Researchers can examine how habitat diversity, fragmentation, or disturbance affect species richness using linear regression.

  4. Carbon Sequestration: Linear regression can be applied to study the relationship between forest characteristics (e.g., tree density, age) and carbon sequestration rates in ecosystems.

7.3.2 Performing Linear Regression

7.3.2.1 Performing linear regression in R

  1. Load Required Packages: Begin by loading necessary packages like tidyverse for data manipulation and lm() for linear modeling.

  2. Load Data: Import your ecological dataset into R.

  3. Fit the Model: Use the lm() function to fit a linear regression model. For example: model <- lm(DV ~ IV1 + IV2, data = dataset), where DV is the dependent variable, IV1 and IV2 are independent variables, and dataset is your data.

  4. View Model Summary: Use summary(model) to view the regression model’s summary, including coefficients, R-squared, and p-values.

  5. Example: The ToothGrowth dataset in R is a built-in dataset that comes with the base R installation. It provides data on the effect of vitamin C on tooth growth in guinea pigs. This dataset is often used for teaching and learning purposes and is useful for practicing various statistical analyses.

  • Here’s some information about the ToothGrowth dataset:

    • Description: The dataset contains observations on the length of guinea pig teeth (tooth growth) under different dosage levels of vitamin C and two delivery methods.

    • Variables:

      • len: The length of tooth growth (in millimeters).

      • supp: The supplement type, either “VC” (vitamin C) or “OJ” (orange juice).

      • dose: The dosage of the supplement in milligrams per day, which can be 0.5, 1.0, or 2.0.

    • Data Structure: The dataset consists of 60 observations.

You can load and access the ToothGrowth dataset in R by simply typing:

# load tooth growth dataset
data("ToothGrowth")

Once loaded, you can explore the dataset using functions like head(ToothGrowth), summary(ToothGrowth), or by creating visualizations and conducting statistical analyses.

This dataset is often used to demonstrate concepts like hypothesis testing, analysis of variance (ANOVA), and regression analysis in introductory statistics and data analysis courses.

# Load necessary R packages using the 'pacman' package
# 'pacman' is a package management tool that makes it easy to load and manage multiple packages at once.
# It installs the packages if they are not already installed and loads them into the R session.
# The 'tidyverse' package includes a collection of packages for data manipulation and visualization.
# The 'report' package is used for generating summary reports.
pacman::p_load(
  tidyverse,    # Load the tidyverse package for data manipulation and visualization.
  report,       # Load the report package for generating summary reports.
  install = TRUE,   # Install the packages if not already installed.
  update = FALSE    # Do not update already installed packages.
)

# Load the ToothGrowth dataset
# The 'ToothGrowth' dataset is included in R and contains data related to the effect of vitamin C on tooth growth in guinea pigs.
data("ToothGrowth")

# Define a linear regression model
# Create a linear regression model using the 'lm' function.
# The model predicts the 'len' (tooth length) variable based on 'supp' (supplement type) and 'dose' (dose level) predictors.
lm_mod1 <- lm(
  len ~ supp + dose,    # Model formula specifying the response variable and predictor variables.
  data = ToothGrowth    # Specify the dataset in which to find the variables.
)

# Show the summary of the linear regression model
# The 'summary' function provides detailed information about the linear regression model, including coefficients, standard errors, t-values, and p-values.
summary(lm_mod1) 
## 
## Call:
## lm(formula = len ~ supp + dose, data = ToothGrowth)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -6.600 -3.700  0.373  2.116  8.800 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  9.2725000  1.2823649   7.231 1.31e-09 ***
## suppVC      -3.7000000  1.0936045  -3.383   0.0013 ** 
## dose         0.0097636  0.0008768  11.135 6.31e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.236 on 57 degrees of freedom
## Multiple R-squared:  0.7038, Adjusted R-squared:  0.6934 
## F-statistic: 67.72 on 2 and 57 DF,  p-value: 8.716e-16
# Extract and print a model output report
# The 'report' package is used here to generate a summary report

R Code Explanation

The codes above load necessary packages and the ToothGrowth dataset, defines a linear regression model, displays a summary of the model using the summary function, and generates a detailed model output report using the report package. The report includes information about the model’s coefficients and statistics related to its fit.

Result/ Report Interpretation

The provided report output contains detailed information about the linear regression model’s performance and parameter estimates. Let’s break down the key interpretations:

  1. Model Explanation:

    • A linear regression model was fitted using Ordinary Least Squares (OLS) to predict tooth length (len) based on two predictors: supp (supplement type) and dose (dose level). The formula used for the model is len ~ supp + dose.

  2. Model Fit:

    • The model is statistically significant and explains a substantial proportion of variance. The key statistics include:

      • R-squared (R²) value of 0.70: This indicates that approximately 70% of the variability in tooth length is explained by the model.

      • F-statistic (F(2, 57)) of 67.72: This tests the overall significance of the model, and the low p-value (< 0.001) suggests that the model is statistically significant.

      • Adjusted R-squared (adj. R²) of 0.69: This adjusts R² for the number of predictors in the model, providing a measure of model fit.

  3. Model Intercept:

    • The model’s intercept corresponds to supp = OJ and dose = 0.

    • The intercept value is 9.27 with a 95% confidence interval (CI) of [6.70, 11.84].

    • The t-statistic (t(57)) is 7.23, and the p-value is < 0.001.

    • This indicates that when supp is OJ, and dose is 0, the estimated average tooth length is 9.27.

  4. Parameter Effects:

    • The report provides information about the effects of individual predictors within the model.

    • The effect of supp (supplement type) with the level [VC] is statistically significant and negative.

      • The beta coefficient is -3.70 with a 95% CI of [-5.89, -1.51].

      • The t-statistic is -3.38, and the p-value is 0.001.

      • The standardized beta (Std. beta) is -0.48.

    • The effect of dose is statistically significant and positive.

      • The beta coefficient is 9.76 with a 95% CI of [8.01, 11.52].

      • The t-statistic is 11.14, and the p-value is < 0.001.

      • The standardized beta (Std. beta) is 0.80.

  5. Standardized Parameters:

    • The standardized parameters were obtained by fitting the model on a standardized version of the dataset. Standardized parameters allow for comparing the relative importance of predictors in different units.

  6. Confidence Intervals and p-values:

    • 95% Confidence Intervals (CIs) and p-values were computed using a Wald t-distribution approximation. These values help assess the precision and statistical significance of parameter estimates.

In summary, the report indicates that the linear regression model is a good fit for explaining tooth length (len) based on the predictors supp and dose. The model’s parameters, including intercept and effects of predictors, are statistically significant and provide valuable insights into the relationship between these variables and tooth length.

A better approach for linear modelling in R is shown as:

# a better stats output summary can be done
lm_mod1 %>% anova(test = "F") %>% report::report()
## The ANOVA suggests that:
## 
##   - The main effect of supp is statistically significant and large (F(1, 57) =
## 11.45, p = 0.001; Eta2 (partial) = 0.17, 95% CI [0.05, 1.00])
##   - The main effect of dose is statistically significant and large (F(1, 57) =
## 123.99, p < .001; Eta2 (partial) = 0.69, 95% CI [0.57, 1.00])
## 
## Effect sizes were labelled following Field's (2013) recommendations.

In the context of linear regression modeling in R, using anova(lm_mod1, test = "F-test") is more appropriate than using summary(lm_mod1) when you want to compare the fit of nested models or assess the overall significance of a group of predictors. Here’s why:

  1. Comparison of Nested Models: anova(lm_mod1, test = "F-test") is particularly useful when you want to compare two or more nested linear regression models. Nested models are those where one model is a subset of the other, typically achieved by adding or removing predictor variables. The F-test provided by anova helps you determine whether the inclusion of additional predictors significantly improves the model fit. This is essential for model selection and assessing the relevance of specific predictors.

  2. Hypothesis Testing for Groups of Predictors: Sometimes, you may want to test the overall significance of a group of predictors rather than examining each predictor individually. The F-test allows you to test the null hypothesis that all the coefficients associated with a specific group of predictors are equal to zero simultaneously. This is useful in scenarios where you have multiple predictors with a similar theoretical basis (e.g., multiple related ecological variables) and want to determine if, collectively, they contribute significantly to explaining the response variable.

  3. Model Comparison: The anova function provides a way to perform statistical tests for model comparison. By comparing nested models or models with different sets of predictors, you can make informed decisions about which variables are essential for explaining the variance in the response variable and which can be omitted. This helps in simplifying models and avoiding overfitting.

In contrast, summary(lm_mod1) typically provides detailed information about the coefficients of the linear regression model, including the estimated coefficients, standard errors, t-values, and p-values for each predictor. While this is valuable for understanding the individual effects of predictors, it doesn’t directly address the questions related to model comparison or the overall significance of groups of predictors.

In summary, anova(lm_mod1, test = "F-test") is a valuable tool for model comparison, assessing the significance of groups of predictors, and making informed decisions about model complexity. It complements the summary function, which is more focused on providing detailed information about individual predictor coefficients.

7.3.2.2 Performing linear regression in Jamovi

Let’s first export the tooth-growth dataset to a csv flat file for use in Jamovi.

  1. Write tooth-growth data with name “toothgrowth.csv” to csv in R.

    # load packages
pacman::p_load(readr, here, install = TRUE, update = F)

# load dataset
data("ToothGrowth")

# save R dataset to csv file
readr::write_csv(
  ToothGrowth,
  file = here::here("docs", "data", "toothgrowth.csv"),
  col_names = TRUE,
  append = FALSE
)

  2. Open/ import the file in Jamovi. In Jamovi, the variable “len” should be a continuous data type, “supp” as nominal and “dose” as continuous.

  3. Go to “Analyses” tab, click “Regression” button and select “Linear Regression”. Perform linear regression by using “len” as the Dependent variable, “supp” in Factors and “dose” as a Covariate. Now compare your results to the previous results generated in R. Interpretations should be the same as those above for R stats.

7.3.3 Interpreting Linear Regression Outputs

  1. Coefficients: Interpret the coefficients of the IVs. A positive coefficient means that as the IV increases, the DV also tends to increase (and vice versa for negative coefficients).

  2. R-squared (R²): R-squared measures the proportion of variance in the DV explained by the IVs. Higher R-squared values indicate a better fit.

  3. P-values: P-values test the null hypothesis that there’s no relationship between IVs and DV. Low p-values (typically < 0.05) indicate statistically significant relationships.

  4. Assumptions: Assess model assumptions, including linearity, independence of errors, homoscedasticity (equal variance of errors), and normality of residuals. Diagnostic plots help check these assumptions. Note that we did not perform any assumptions assessments prior to running the model. We’ll incorporate this workflow in later models.

In ecological research, linear regression provides valuable insights into the relationships between ecological variables. It helps answer questions about ecological processes and how they are influenced by environmental factors. Proper interpretation of model results and assessment of assumptions are crucial for robust ecological conclusions.

7.4 Logistic Regression

Definition: Logistic regression is a statistical method used to model the probability of a binary outcome variable (0/1, Yes/No, True/False) as a function of one or more independent variables. It’s particularly useful when the dependent variable represents a categorical response with two levels.

7.4.1 Applications in Ecological Research

  1. Species Presence/Absence: Logistic regression is widely used in ecology to model the probability of species presence or absence based on environmental factors such as temperature, habitat type, or elevation.

  2. Habitat Suitability: Ecologists can employ logistic regression to determine the suitability of habitats for specific species. For example, modeling the presence of a particular bird species in relation to forest cover or proximity to water sources.

  3. Biodiversity Conservation: Logistic regression can help predict the likelihood of the presence of endangered species in different regions based on factors like land use, climate, or protected areas.

  4. Disease Spread: In disease ecology, logistic regression can be used to model the probability of disease occurrence in relation to environmental variables, aiding in the understanding and management of disease spread.

7.4.2 Performing Logistic Regression

7.4.2.1 Using R for Logistic Regression

# Load necessary libraries (if not already loaded)
pacman::p_load(
  tidyverse, 
  flextable, 
  install = T, 
  update = F
)

# Load the ToothGrowth dataset
data("ToothGrowth")

# Perform logistic regression using glm
logistic_mod <-
  glm(supp ~ len + dose, data = ToothGrowth, family = "binomial")

# Output analysis of deviance table as a formatted flextable
logistic_mod %>% 
  anova(test = "LRT") %>%                # Perform an analysis of deviance
  tibble::rownames_to_column(., var = "Predictors") %>%  # Add a column for predictor names
  flextable::qflextable()                 # Create a formatted flextable

Predictors

Df

Deviance

Resid. Df

Resid. Dev

Pr(>Chi)

NULL

59

83.18

len

1

3.64

58

79.53

0.06

dose

1

7.20

57

72.33

0.01

R Code Explanation

  1. Library Loading: This section loads the necessary R libraries, including the tidyverse package for data manipulation and visualization.

  2. Dataset Loading: The data("ToothGrowth") command loads the ToothGrowth dataset into your R session. This dataset contains information about the effect of vitamin C dose on tooth growth in Guinea pigs.

  3. Logistic Regression: Logistic regression is performed using the glm function. It models the relationship between the binary variable supp (supplement type) and the predictor variables len (tooth length) and dose (dose of vitamin C). The family argument is set to “binomial” to specify logistic regression.

  4. Analysis of Deviance: The anova function is used to perform an analysis of deviance on the logistic regression model, assessing the significance of variables in the model. The anova(test = "LRT") code calls the anova function on the logistic regression model (logistic_mod) specifying the type of test to be performed, which is the likelihood ratio test (LRT). The LRT is used to compare the fit of two nested models: one with the predictors and one without.

    • Here’s what the likelihood ratio test (LRT) does in the context of logistic regression:

      1. It compares two models:

        • The null model (reduced model): This is a model that includes only an intercept (no predictors).

        • The full model: This is the logistic regression model you have fitted (logistic_mod) with one or more predictor variables.

      2. The LRT assesses whether the full model (with predictors) provides a significantly better fit to the data compared to the null model (with no predictors).

      3. The test statistic for the LRT follows a chi-squared distribution, and its significance is assessed by comparing it to a chi-squared distribution with degrees of freedom equal to the difference in the number of parameters estimated between the two models.

      4. The output typically includes the chi-squared test statistic, degrees of freedom, and the associated p-value. The p-value tells you whether the addition of the predictors significantly improves the model fit.

      In summary, the line logistic_mod %>% anova(test = "LRT") is used to perform a likelihood ratio test on the logistic regression model to assess the overall significance of the predictors in improving the model’s fit compared to a null model. If the p-value is below a chosen significance level (e.g., 0.05), it suggests that the predictors collectively have a significant impact on the response variable.

  5. Data Manipulation: The %>% operator is used to pipe the results of the analysis into a series of data manipulation and formatting functions.

    • tibble::rownames_to_column(., var = "Predictors") adds a column named “Predictors” to the output, containing predictor variable names.

    • flextable::qflextable() creates a formatted flextable, which can be used for generating tables with a customized appearance.

Overall, this code performs logistic regression, analyzes the deviance, and presents the results in a formatted table for better readability and interpretation.

Interpretation

Interpretation for the logistic regression output generated by the following R code chunk is defined below.

logistic_mod %>% 
  anova(test = "LRT")

The “Analysis of Deviance” table provides information about the statistical significance of the predictor variables in a logistic regression model. Here’s how to interpret the table:

  • Model Information: The table begins with some general information about the logistic regression model:

    • Model type: “binomial” indicates that it’s a binary logistic regression.

    • Link function: “logit” refers to the log-odds link function used in logistic regression.

    • Response variable: “supp” is the variable being predicted.

  • Sequential Analysis: The table then lists the predictor variables (“len” and “dose”) added sequentially from first to last. Each variable’s impact on the model is assessed in turn.

  • Df (Degrees of Freedom): The “Df” column indicates the degrees of freedom associated with each variable. For “len” and “dose,” there is 1 degree of freedom each.

  • Deviance: The “Deviance” column shows the deviance associated with each variable. Deviance is a measure of how well the model fits the data. It’s similar to the residual sum of squares in linear regression. Smaller values indicate a better fit.

  • Resid. Df (Residual Degrees of Freedom): The “Resid. Df” column represents the degrees of freedom associated with the residuals after including each variable in the model. It’s calculated as the total degrees of freedom minus the degrees of freedom associated with the variable.

  • Resid. Dev (Residual Deviance): The “Resid. Dev” column shows the residual deviance after including each variable in the model. Like deviance, smaller values indicate a better fit.

  • Pr(>Chi): The “Pr(>Chi)” column provides the p-value associated with each variable’s contribution to the model. This p-value represents the probability of observing a deviance statistic as extreme as, or more extreme than, the one calculated if the variable had no effect on the response. Smaller p-values suggest stronger evidence against the null hypothesis that the variable has no effect.

  • Significance Codes: Significance codes are used to indicate the level of statistical significance of each variable’s contribution to the model. They are often represented as asterisks (*). In this table:

    • “0.001” corresponds to ‘***,’ indicating extremely high significance.

    • “0.01” corresponds to ‘**,’ indicating high significance.

    • “0.05” corresponds to ‘*,’ indicating moderate significance.

    • “0.1” corresponds to a space (’ ’), indicating marginal significance.

    • “1” indicates that the variable is not statistically significant.

Interpretation

  • The initial model (NULL model) does not include any predictors and has a deviance of 83.178 with 59 degrees of freedom.

  • When the “len” variable is added to the model, it reduces the deviance by 3.6436 units with 1 degree of freedom. The p-value associated with “len” is 0.056286, which is greater than the typical significance level of 0.05. Therefore, “len” is not statistically significant at the 0.05 level.

  • When the “dose” variable is added to the model, it further reduces the deviance by 7.2043 units with 1 degree of freedom. The p-value associated with “dose” is 0.007273, which is less than 0.05. Therefore, “dose” is statistically significant at the 0.05 level.

In summary, the analysis of deviance indicates that the “dose” variable is statistically significant in predicting the “supp” variable, while the “len” variable is not statistically significant at the 0.05 significance level.

7.4.2.2 Using Jamovi for Logistic Regression

  • From the “Analyses” tab, select 2 Outcomes (binomial under logistic regression). Compare results and interpretation to R outputs.

7.4.3 Interpreting Logistic Regression Outputs

  1. Coefficients: Interpret the coefficients of the IVs. Positive coefficients indicate an increase in the log-odds of the binary outcome, while negative coefficients indicate a decrease.

  2. Odds Ratios: Exponentiate the coefficients to get odds ratios. An odds ratio greater than 1 indicates an increase in the odds of the outcome, and less than 1 indicates a decrease.

  3. P-values: P-values test the null hypothesis that there’s no relationship between IVs and the binary outcome. Low p-values (typically < 0.05) indicate statistically significant relationships.

Logistic regression is a valuable tool in ecological research for modeling binary outcomes and understanding the factors influencing ecological phenomena like species presence, habitat suitability, and disease occurrence. Proper interpretation of model results is essential for making ecologically meaningful conclusions.

7.5 Model Assessment and Selection

7.5.1 Assessing Model Fit

  1. Residual Analysis: Residuals are the differences between the observed and predicted values. In regression analysis, it’s crucial to assess the distribution of residuals. A well-fitting model should have residuals that are normally distributed with mean zero. You can visualize residuals using residual plots, such as scatterplots of residuals against predicted values or against independent variables. Deviations from normality or patterns in these plots can indicate issues with model fit.

  2. R-squared (Coefficient of Determination): R-squared measures the proportion of variance in the dependent variable explained by the model. Higher R-squared values indicate better model fit, but it’s important to balance model complexity with model fit.

  3. Adjusted R-squared: Adjusted R-squared accounts for the number of predictors in the model, penalizing models with too many predictors. It helps prevent overfitting by adjusting R-squared for the number of predictors.

  4. Residual Sum of Squares (RSS) and Deviance: These measures represent the sum of squared differences between observed and predicted values. Smaller values indicate better fit.

  5. p-values of Coefficients: Low p-values suggest that predictor variables are statistically significant in explaining the variation in the dependent variable. High p-values indicate that a variable may not be relevant.

7.5.2 Illustrating Residual Analysis

Residual analysis involves examining plots of residuals to identify patterns or outliers. For instance, you might create:

  • Residual vs. Fitted Value Plot: To check for linearity and constant variance of residuals.
# Load necessary libraries (if not already loaded)
pacman::p_load(
  tidyverse, 
  easystats, 
  car,
  install = T, update = F
)

# Load the ToothGrowth dataset
data("ToothGrowth")

# Fit a linear regression model
lm_mod1 <- lm(len ~ supp + dose, data = ToothGrowth)

# Create a Residual vs. Fitted Value Plot
plot(lm_mod1, which = 1, main = "Residual vs. Fitted Value Plot")

R Code Explanation

The provided R code is for creating a “Residual vs. Fitted Value Plot” to assess the relationship between the residuals (the differences between the observed and predicted values) and the fitted values (the values predicted by the regression model). This plot is used to check whether the linear regression assumptions, particularly the assumption of homoscedasticity (constant variance of residuals), are met.

Here’s what each part of the code does:

  1. Loading Libraries: The code begins by loading several R libraries. These libraries include:

    • tidyverse: A collection of packages for data manipulation and visualization.

    • easystats: A package for easy and consistent statistical reporting.

    • car: The “car” package, which provides various diagnostic tools for regression analysis.

  2. Loading Data: The data("ToothGrowth") command loads the “ToothGrowth” dataset, which is a built-in dataset in R. This dataset contains measurements of tooth length in guinea pigs.

  3. Fitting a Linear Regression Model: The code fits a linear regression model (lm_mod1) to the data. This model predicts tooth length (len) based on two predictor variables: supp (supplement type) and dose (dose of the supplement).

  4. Creating the Residual vs. Fitted Value Plot: The plot() function is used to create the Residual vs. Fitted Value Plot for the linear regression model. The arguments provided to plot() are as follows:

    • lm_mod1: The fitted linear regression model.

    • which = 1: Specifies that you want to create the Residual vs. Fitted Value Plot.

    • main = "Residual vs. Fitted Value Plot": Sets the main title of the plot.

The resulting plot will display the residuals on the vertical axis and the fitted (predicted) values on the horizontal axis. Each point on the plot represents an observation from the dataset. The plot helps you assess whether the residuals have a consistent spread across different fitted values, which is crucial for the validity of linear regression assumptions. A horizontal band or cloud of points with no discernible pattern indicates that the assumption of homoscedasticity is likely met. If there is a pattern or funnel shape in the plot, it suggests heteroscedasticity, which may violate the assumption.

In summary, this code segment allows you to create a diagnostic plot to assess the homoscedasticity assumption in a linear regression model using the “ToothGrowth” dataset.

  • Normal Probability Plot: To assess the normality of residuals.
# Load necessary libraries (if not already loaded)
pacman::p_load(
  tidyverse, 
  easystats, 
  car,
  install = T, update = F
)

# Load the ToothGrowth dataset
data("ToothGrowth")

# Fit a linear regression model
lm_mod1 <- lm(len ~ supp + dose, data = ToothGrowth)

# Create a Normal Probability Plot (Q-Q Plot) for residuals
qqnorm(residuals(lm_mod1), main = "Normal Probability Plot (Q-Q Plot) of Residuals")
qqline(residuals(lm_mod1), col = "red")

R Code Explanation

The provided R code is for creating a “Normal Probability Plot” (also known as a Q-Q Plot) to assess whether the residuals of a linear regression model follow a normal distribution. This plot is used to check the assumption of normality of residuals.

Here’s an explanation of each part of the code:

  1. Loading Libraries: The code starts by loading several R libraries using the pacman::p_load() function. These libraries include:

    • tidyverse: A collection of packages for data manipulation and visualization.

    • easystats: A package for easy and consistent statistical reporting.

    • car: The “car” package, which provides various diagnostic tools for regression analysis.

  2. Loading Data: The data("ToothGrowth") command loads the “ToothGrowth” dataset, which contains measurements of tooth length in guinea pigs. This dataset will be used for fitting a linear regression model and assessing its residuals.

  3. Fitting a Linear Regression Model: The code fits a linear regression model (lm_mod1) to the data. This model predicts tooth length (len) based on two predictor variables: supp (supplement type) and dose (dose of the supplement).

  4. Creating the Normal Probability Plot (Q-Q Plot) for Residuals:

    • qqnorm(residuals(lm_mod1), main = "Normal Probability Plot (Q-Q Plot) of Residuals"): This line of code generates the Q-Q Plot for the residuals of the linear regression model. The qqnorm() function is used to create the Q-Q Plot, and residuals(lm_mod1) extracts the residuals from the model. The main argument sets the main title of the plot.

    • qqline(residuals(lm_mod1), col = "red"): This line adds a reference line to the Q-Q Plot. The qqline() function is used to add a line to the plot to help assess how closely the residuals follow a normal distribution. In this case, the line is colored red for visibility.

The resulting Q-Q Plot displays the quantiles of the observed residuals against the quantiles of a theoretical normal distribution. If the residuals closely follow a normal distribution, the points on the plot will closely align with the reference line (red line). Deviations from the line may indicate departures from normality.

In summary, this code segment allows you to create a Q-Q Plot to visually assess the normality assumption of the residuals of a linear regression model using the “ToothGrowth” dataset.

  • Residual vs. Predictor Variable Plot: To look for patterns in residuals concerning predictor variables.
# Load necessary libraries (if not already loaded)
pacman::p_load(
  tidyverse, 
  easystats, 
  car,
  install = T, update = F
)

# Load the ToothGrowth dataset
data("ToothGrowth")

# Fit a linear regression model
lm_mod1 <- lm(len ~ supp + dose, data = ToothGrowth)

# Create a Residual vs. Predictor Variable Plot
car::residualPlots(lm_mod1, col.quad = "red")

##            Test stat Pr(>|Test stat|)    
## supp                                     
## dose         -3.7144        0.0004714 ***
## Tukey test   -4.5770        4.717e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

R Code Explanation

  1. Loading Libraries: This code begins by loading several R libraries using the pacman::p_load() function. These libraries include:

    • tidyverse: A collection of packages for data manipulation and visualization.

    • easystats: A package for easy and consistent statistical reporting.

    • car: The “car” package, which provides various diagnostic tools for regression analysis.

  2. Loading Data: The data("ToothGrowth") command loads the “ToothGrowth” dataset, which contains measurements of tooth length in guinea pigs. This dataset will be used for fitting a linear regression model and assessing its residuals.

  3. Fitting a Linear Regression Model: The code fits a linear regression model (lm_mod1) to the data. This model predicts tooth length (len) based on two predictor variables: supp (supplement type) and dose (dose of the supplement).

  4. Creating the Residual vs. Predictor Variable Plot:

    • car::residualPlots(lm_mod1, col.quad = "red"): This line of code generates the Residual vs. Predictor Variable Plot using the residualPlots() function from the “car” package. The lm_mod1 model is passed as an argument. The col.quad = "red" argument specifies that points outside a certain range will be colored red. This plot helps visualize the relationship between the residuals and the predictor variables.

The resulting plot displays the relationship between the residuals and the predictor variables in the linear regression model. It can be used to identify patterns or trends in the residuals, such as heteroscedasticity or nonlinearity.

In summary, this code segment allows you to create a Residual vs. Predictor Variable Plot for a linear regression model fitted to the “ToothGrowth” dataset, which can be useful for diagnosing potential issues with the model’s assumptions.

  • Leverage Plot: To identify influential observations that have a significant impact on the model.
# Load necessary libraries (if not already loaded)
pacman::p_load(
  tidyverse, 
  easystats, 
  car,
  install = T, update = F
)

# Load the ToothGrowth dataset
data("ToothGrowth")

# Fit a linear regression model
lm_mod1 <- lm(len ~ supp + dose, data = ToothGrowth)

# Create a Leverage Plot
car::leveragePlots(lm_mod1, col.lines = "red")

R Code Explanation

  1. Loading Libraries: This code begins by loading several R libraries using the pacman::p_load() function, just like in the previous example. These libraries include tidyverse, easystats, and car, which are used for data manipulation, statistical reporting, and regression analysis.

  2. Loading Data: The data("ToothGrowth") command loads the “ToothGrowth” dataset, which contains measurements of tooth length in guinea pigs. This dataset will be used for fitting a linear regression model and assessing its leverage.

  3. Fitting a Linear Regression Model: The code fits a linear regression model (lm_mod1) to the data. This model predicts tooth length (len) based on two predictor variables: supp (supplement type) and dose (dose of the supplement).

  4. Creating the Leverage Plot:

    • car::leveragePlots(lm_mod1, col.lines = "red"): This line of code generates the Leverage Plot using the leveragePlots() function from the “car” package. The lm_mod1 model is passed as an argument. The col.lines = "red" argument specifies that lines corresponding to specific observations with high leverage will be colored red.

The resulting plot displays the leverage values for each observation in the dataset. High-leverage observations are typically those that have a strong influence on the regression model’s coefficients. The red lines on the plot help identify observations with high leverage.

In summary, this code segment allows you to create a Leverage Plot for a linear regression model fitted to the “ToothGrowth” dataset, helping you identify influential observations in the model.

7.5.3 Model Selection

7.5.3.1 Process of Model Selection

  1. Start with a Simple Model: Begin with a simple model that includes only essential predictor variables.

  2. Add Complexity: Gradually add complexity by including additional predictors or higher-order terms (e.g., quadratic terms) if necessary. Assess whether the added complexity improves model fit.

  3. Compare Models: Use information criteria like AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion) to compare different models. Lower AIC and BIC values indicate better-fitting models, with a balance between goodness of fit and model complexity.

  4. Cross-Validation: Perform cross-validation, like k-fold cross-validation, to assess how well the model generalizes to new data. This helps avoid overfitting.

  5. Domain Knowledge: Consider ecological domain knowledge when selecting the most appropriate model. Sometimes, theoretical understanding of the system can guide model selection.

7.5.3.2 AIC and BIC for Model Comparison

  • Akaike Information Criterion (AIC): AIC estimates the relative quality of statistical models. It penalizes models for their complexity. Smaller AIC values indicate better-fitting models, but AIC does not provide an absolute measure of model fit.

  • Bayesian Information Criterion (BIC): BIC, similar to AIC, penalizes models for complexity. However, it applies a stronger penalty for additional parameters. Like AIC, lower BIC values indicate better-fitting models.

In ecological research, assessing model fit and selecting the most appropriate model are critical steps to ensure that the regression analysis accurately captures the underlying relationships in the data. Residual analysis and information criteria like AIC and BIC provide valuable tools for model evaluation and selection.

7.6 Conclusion

In conclusion, Chapter 5 has been a comprehensive journey into the world of regression analysis, tailored for ecological research. Here are the key takeaways:

  1. Fundamentals of Regression: You’ve grasped the fundamental concepts of regression analysis, understanding how it models relationships between variables. This knowledge forms the foundation for exploring ecological data.

  2. Linear Regression: You’ve delved into linear regression, a powerful tool for modeling linear relationships between variables. Real-world examples have shown you how to apply this technique to ecological questions.

  3. Logistic Regression: Logistic regression has been introduced as a means to model binary outcomes in ecological contexts. You’ve seen its applications and how to interpret results.

  4. Model Assessment: You’ve learned the importance of assessing model fit, employing techniques like residual analysis, R-squared, and p-values to validate your models. These tools ensure your models accurately represent the data.

  5. Model Selection: Model selection strategies, including starting simple, adding complexity, and using information criteria like AIC and BIC, have been highlighted. You’re now equipped to choose the most appropriate model for your ecological research.

  6. Continuous Learning: Remember that regression analysis is a dynamic field. Stay curious, continue learning, and consider domain-specific knowledge to enhance the relevance and accuracy of your models.

This chapter empowers you with the skills to navigate and model ecological relationships effectively. Whether you’re exploring linear associations or tackling binary outcomes, you now have the tools to build, assess, and interpret regression models. These models are invaluable for gaining insights in ecological research, enabling you to make data-driven decisions and contribute to the understanding of complex ecological systems.

8 Chapter 6: Data Visualization

8.1 …. [in progress]

9 Chapter 7: Advanced Topics

9.1 …. [in progress]

10 Chapter 8: Case Studies

10.1 …. [in progress]

10.2 Real-World Dataset and Exercise

In this exercise we will perform a simple hypothesis test using real-world data set. Data used in this exercise was extracted from the mendeley database (Win, Kyaw (2023), “Aboveground Tree Carbon of Teak Plantations in West Bago Mountains, Myanmar”, Mendeley Data, V1, doi: 10.17632/3xvcfskhwz.1): Aboveground Tree Carbon of Teak Plantations in West Bago Mountains, Myanmar.

10.3 Import and explore the dataset in Jamovi

Steps

  1. Open “Filtered.sav” file in Jamovi. The data should already be placed in the “data” sub-directory.

    open .sav file

  2. Go to the “Variables” tab and remove the last four columns/ variables as we won’t use them.

    remove columns

  3. Go to the “Data” tab and change the “Plantation_age” data/ measure type to “ordinal” via the “Setup” button. Change data types

  4. Navigate to the “Analyses” tab and from the “Exploration” button select “Descriptives”. Use the functions from this window to explore the data set. Perform data exploration (descriptive) on the selected variable.

  5. You can further perform data exploration visually. Select the “scatterplot” from the “Exploration” button and insert the appropriate variables to generate a scatterplot with linear fits along with density plots. Linear and density plots

  6. You can also perform correlation test including other statistical tests.

10.4 Performing hypothesis test in Jamovi

  1. Formulating the Hypothesis: To assess the impact of plantation age on above-ground tree carbon content, we formulate our hypotheses:

    • Null Hypothesis (Ho): There are no significant differences in above-ground tree carbon content among different plantation ages.

    • Alternative Hypothesis (Ha): There are significant differences in above-ground tree carbon content among different plantation ages.

  2. Selecting the Appropriate Test: To scrutinize these hypotheses, we opt for a two-way ANOVA. This choice aligns with our research objectives as we intend to explore variations in above-ground carbon content across multiple plantation ages.

  3. Addressing Data Normality: As a prerequisite for conducting an ANOVA, we assess the normality of our response variable, ‘Aboveground_Tree_Carbon_ton_per_ha_per_year,’ using the Shapiro-Wilk test. The outcome reveals a significant effect (p < 0.001), implying that this variable doesn’t adhere to a normal distribution. Consequently, we pivot to the non-parametric equivalent, the “Kruskal-Wallis” test, as a robust alternative.Perform normality test on the responds variable.

  4. Executing the Kruskal-Wallis Test: Navigating to the Analysis tab, we select the ANOVA button and then opt for the “Kruskal-Wallis” test from the non-parametric section. The results uncover a significant effect of plantation age on carbon content (p < .001). This substantiates the presence of meaningful disparities in carbon content across plantation ages.

  5. Unearthing Specific Differences: To pinpoint where these differences manifest, we proceed with a pairwise comparison. This step elucidates the precise distinctions in carbon content among different plantation ages.Kruskal-Wallis test and pairwise comparison.

  6. Visualizing Results: To provide a more intuitive understanding, we employ box plots as a visual aid. These plots vividly display the variations in above-ground tree carbon content across different plantation ages, enhancing our ability to interpret and communicate the findings.Boxplots.

12 Supplementary Information

12.1 Hypothesis Testing: Parametric and Non-Parametric Tests

Understanding the Foundations of Statistical Testing

12.1.1 Importance of Hypothesis Testing in Forestry and Ecology

Hypothesis testing plays a pivotal role in the fields of forestry and ecology, offering invaluable insights into various aspects of environmental and ecological research. This statistical methodology allows researchers to systematically investigate hypotheses, evaluate the validity of theories, and draw meaningful conclusions based on empirical evidence. Below, we delve into the significance of hypothesis testing in forestry and ecology:

  1. Validating Theories: Forestry and ecology encompass a wide range of complex theories and models that describe the behavior of ecosystems, species, and natural resources. Hypothesis testing provides a rigorous framework to assess the accuracy of these theories by comparing predicted outcomes to observed data. Researchers can confirm whether their theoretical predictions align with real-world observations, enhancing the credibility of their work.

  2. Informed Decision-Making: In both forestry and ecology, critical decisions are made concerning the management of natural resources, conservation efforts, and environmental policies. Hypothesis testing allows researchers to collect and analyze data systematically, providing a scientific basis for these decisions. For example, hypotheses about the effects of specific management practices on forest regeneration can guide forest management strategies.

  3. Environmental Impact Assessment: Understanding the influence of environmental factors on ecosystems and species is fundamental in ecology. Hypothesis testing enables scientists to investigate how variables such as temperature, precipitation, pollution, or habitat loss affect ecological systems. This information is crucial for assessing environmental impacts, predicting trends, and implementing measures to mitigate negative consequences.

  4. Species Conservation: Conservation biology is a vital component of ecology. Hypothesis testing aids in assessing the success of conservation efforts and understanding the factors influencing endangered species. Researchers can formulate hypotheses related to the effectiveness of conservation strategies, such as habitat restoration or captive breeding programs, and rigorously test these hypotheses through data analysis.

  5. Biodiversity Studies: Hypothesis testing is instrumental in biodiversity studies. Ecologists can develop hypotheses about the factors contributing to biodiversity, including species interactions, habitat diversity, and environmental conditions. Through hypothesis testing, researchers can identify key drivers of biodiversity patterns and develop strategies to protect and preserve diverse ecosystems.

Hypothesis testing is an indispensable tool in forestry and ecology, providing researchers with a structured approach to explore and validate theories, make informed decisions, assess environmental impacts, conserve species, and study biodiversity. By subjecting hypotheses to rigorous statistical analysis, scientists contribute to a deeper understanding of the natural world and support evidence-based practices in these critical fields.

12.1.2 Key Concepts

12.1.2.1 Definition of Null and Alternative Hypotheses

  • Null Hypothesis (H0): The null hypothesis serves as the baseline assumption in hypothesis testing. It posits that there is no statistically significant difference or effect in the population under investigation. In the context of oak tree height, the null hypothesis (H0) could be framed as: “There is no significant difference in the average height of oak trees between Site A and Site B.” In essence, it suggests that any observed differences are due to random variation.

  • Alternative Hypothesis (H1): The alternative hypothesis is the statement researchers seek to support. It proposes the existence of a significant difference, effect, or relationship within the population. For our example, the alternative hypothesis (H1) could be stated as: “There is a significant difference in the average height of oak trees between Site A and Site B.” This implies that the observed differences are not due to chance but are indeed meaningful.

12.1.2.2 Explanation of the Significance Level (Alpha)

  • Significance Level (Alpha): The significance level, often denoted as α (alpha), represents the threshold for statistical significance. In most research, it is set at 0.05 (5%). This value signifies the maximum acceptable probability of making a Type I error — wrongly rejecting the null hypothesis when it is true. In practical terms, it means that researchers are willing to tolerate a 5% chance of making this error.

12.1.2.3 Introducing p-values and Their Interpretation

  • p-value: The p-value quantifies the evidence against the null hypothesis. It represents the probability of obtaining observed results, or more extreme results, when the null hypothesis is true. A low p-value suggests that the observed data is unlikely to have occurred by random chance alone.

  • Interpretation of p-values: In our example, a p-value of 0.03 indicates that there’s a 3% probability that the observed difference in oak tree heights between Site A and Site B occurred due to random chance. Since this probability (3%) is less than the significance level (5%), we would typically reject the null hypothesis in favor of the alternative hypothesis, suggesting a significant difference.

Type I and Type II Errors

  • Type I Error: In ecology, a Type I error could have significant consequences. It occurs when researchers incorrectly identify a species as invasive when it is not. This could lead to unwarranted and potentially costly eradication efforts or management strategies.

  • Type II Error: Conversely, a Type II error in ecology might involve failing to detect a critically endangered species when it does exist. This error could result in the inadequate protection of a vulnerable species and its habitat.

In summary, understanding null and alternative hypotheses, the significance level (alpha), p-values, and the potential for Type I and Type II errors is crucial in ecological research. These concepts guide researchers in making informed decisions about the validity of their findings and the implications for conservation, species identification, and ecosystem management.

12.1.3 Parametric vs. Non-Parametric Tests

12.1.3.1 Difference between Parametric and Non-Parametric Tests

  • Parametric Tests: Parametric tests make specific assumptions about the distribution of data, often assuming it follows a normal distribution. These tests rely on parameters like means and variances.

  • Non-Parametric Tests: Non-parametric tests, on the other hand, are distribution-free and do not rely on specific assumptions about the data distribution. They are more robust when data deviates from normality or when dealing with ordinal or non-continuous data.

12.1.3.2 Examples in Forestry and Ecology

  • Parametric Example: Testing if there’s a difference in the mean chlorophyll levels between two groups of plant species. Here, you might assume that chlorophyll levels follow a normal distribution.

  • Non-Parametric Example: Comparing the diversity of aquatic invertebrate species in different river habitats. Since species diversity may not follow a normal distribution, a non-parametric test is more appropriate.

12.1.3.3 Parametric Tests

12.1.3.3.1 When to Use Parametric Tests

Parametric tests are appropriate when data is normally distributed and meets the assumptions of the specific test being used. These tests tend to be more powerful when assumptions are met.

12.1.3.3.2 Common Parametric Tests with Forestry/Ecology Examples:

  • t-test: Use a t-test when comparing the mean annual precipitation in two different forest ecosystems. This test assesses if the means of two groups are significantly different.

  • ANOVA (Analysis of Variance): ANOVA is suitable for assessing if there’s a significant difference in bird species richness among three different forest types. It can compare means across multiple groups.

  • Linear Regression: Linear regression is ideal for investigating the relationship between temperature and tree growth in a specific forest region. It models the relationship between two continuous variables.

12.1.3.4 Non-Parametric Tests

12.1.3.4.1 When to Use Non-Parametric Tests

Non-parametric tests should be employed when data doesn’t meet parametric assumptions, such as non-normality, or when dealing with ordinal or ranked data.

12.1.3.4.2 Common Non-Parametric Tests with Forestry/Ecology Examples

  • Mann-Whitney U Test: Use this test to compare the diversity of fungi species in two different soil types. It assesses if there’s a difference in the distribution of values between two groups.

  • Kruskal-Wallis Test: When you want to test if there’s a difference in plant height across various altitudinal zones, the Kruskal-Wallis test is suitable. It’s a non-parametric alternative to ANOVA for multiple groups.

  • Wilcoxon Signed-Rank Test: Assess changes in insect abundance before and after a controlled burn in a grassland ecosystem. This non-parametric test is used for paired data to determine if the medians are different.

Understanding the choice between parametric and non-parametric tests is essential in forestry and ecology research. Parametric tests make specific assumptions about data distribution, while non-parametric tests are more flexible and suitable when assumptions are not met or when dealing with non-continuous data. The choice of test should align with the nature of the data and the research question.

12.1.4 Considerations for Choosing Between Parametric and Non-Parametric Tests in Forestry and Ecology

  1. Data Characteristics

    • Normality: If your data follows a normal distribution and meets the assumptions of parametric tests, then parametric tests can provide more statistical power. Ensure you check normality using tools like normal probability plots or Shapiro-Wilk tests.

    • Data Type: Consider the type of data you have. Parametric tests are designed for continuous, interval, or ratio data. Non-parametric tests can handle ordinal or ranked data and are robust to outliers.

  2. Sample Size

    • Large Samples: Parametric tests tend to perform well with larger sample sizes. If you have a substantial amount of data, parametric tests may detect even small differences.

    • Small Samples: In cases with small sample sizes, non-parametric tests can be more appropriate. They are less sensitive to outliers and deviations from normality.

  3. Research Questions

    • Nature of Comparison: The nature of your research question matters. If you’re comparing means or conducting regression analysis, parametric tests are common. For comparing distributions or medians, non-parametric tests are often preferred.

    • Experimental Design: The design of your study, such as whether it’s a repeated-measures design or an independent measures design, can influence test choice. Some tests, like the paired t-test, are parametric and have non-parametric counterparts.

  4. Assumptions

    • Assumption Check: Always check the assumptions of parametric tests, such as normality and homogeneity of variances. If assumptions are violated, consider non-parametric alternatives.

  5. Robustness

    • Robustness to Outliers: Non-parametric tests are less affected by outliers. If your data includes extreme values, non-parametric tests may provide more reliable results.

  6. Type of Data Analysis

    • Regression: If you’re conducting regression analysis, parametric linear regression models are widely used. Non-parametric regression techniques, like kernel regression, exist but are less common.

  7. Statistical Power

    • Statistical Power: Consider the balance between statistical power and assumptions. Parametric tests tend to have higher power when assumptions are met, but lower power when assumptions are violated.

  8. Interpretability

    • Interpretability: Think about the ease of interpretation. Parametric tests often provide straightforward interpretations, such as differences in means. Non-parametric tests may yield results that are less intuitive to interpret.

  9. Data Transformations

    • Data Transformations: If your data doesn’t meet parametric assumptions, consider data transformations to achieve normality. However, be cautious with transformations, as they can impact interpretation.

The choice between parametric and non-parametric tests in forestry and ecology should be driven by a thorough understanding of your data, research questions, and assumptions. While parametric tests offer higher power under specific conditions, non-parametric tests provide robustness when assumptions are in doubt. It’s essential to carefully consider these factors to make informed decisions about test selection in your research.

12.1.5 Practical Example

12.1.5.1 Comparing Canopy Cover in Logged and Old-Growth Forests

  • Research Question: Does the average tree canopy cover differ significantly between a logged forest and an old-growth forest?

  • Data: Canopy cover measurements from both forest types.

  • Hypotheses:

    • Null Hypothesis (H0): There is no difference in canopy cover between the logged forest and the old-growth forest.

    • Alternative Hypothesis (H1): There is a significant difference in canopy cover between the logged forest and the old-growth forest.

  • Steps to Analyze:

  1. Data Collection: Gather canopy cover measurements for both the logged and old-growth forests. Ensure that the data is properly recorded and labeled.

  2. Data Inspection: Start by inspecting the data. Plot histograms or density plots to assess data distribution. You may use tools in R or Jamovi for this purpose.

  3. Choosing the Test: Based on the data distribution:

    • If the data follows a normal distribution and meets the assumptions (check using normality tests), you can perform a t-test.

    • If the data does not meet the assumptions of normality, consider a Mann-Whitney U test (a non-parametric alternative).

  4. Perform the Test:

    • In R: Use the t.test() function for the t-test or wilcox.test() function for the Mann-Whitney U test.

    • In Jamovi: You can use the point-and-click interface to perform these tests. Import your data and choose the appropriate test based on data distribution.

  5. Interpret Results:

    • For the t-test, examine the p-value. If it is less than your chosen significance level (typically 0.05), you would reject the null hypothesis. This suggests that there is a significant difference in canopy cover between the logged and old-growth forests.

    • For the Mann-Whitney U test, similarly look at the p-value. A p-value below 0.05 indicates a significant difference in canopy cover.

  6. Effect Size: Consider calculating and reporting the effect size. For example, in a t-test, Cohen’s d is a commonly used measure of effect size.

  7. Conclude: Based on the results, draw a conclusion regarding whether there is a significant difference in canopy cover between the two forest types.

  8. Report: Document your findings in a clear and concise manner, including any visualizations and statistical details. Mention the test used, the p-value, and the effect size.

  9. Discussion: Discuss the implications of your findings for forestry and ecology. Consider how this information can contribute to the understanding of forest ecosystems or conservation efforts.

Remember that the choice between the t-test and Mann-Whitney U test depends on the data distribution and assumptions. Always verify the assumptions before selecting the appropriate test.

12.1.6 Summary

12.1.6.1 The Significance of Hypothesis Testing in Forestry and Ecology

  • Hypothesis Testing’s Fundamental Role: Hypothesis testing is a cornerstone of data analysis in forestry and ecology. It empowers researchers to make informed decisions, draw meaningful conclusions, and contribute to the understanding of ecological systems and forest management.

  • Data-Driven Decision Making: In forestry and ecology, decisions regarding conservation efforts, ecosystem management, and environmental policy are often data-driven. Hypothesis testing provides a systematic approach to validate or refute hypotheses, which, in turn, guide these critical decisions.

  • Tailoring Tests to Data: The choice of a hypothesis test is not arbitrary but depends on the specific characteristics of the data at hand. Researchers need to assess data distribution, sample size, and the nature of variables before selecting an appropriate statistical test.

  • The Crucial Role of Hypothesis Formulation: The formulation of null and alternative hypotheses should be done with precision. It’s imperative to clearly articulate the research question and the expected outcomes in the hypotheses. Ambiguity in hypothesis formulation can lead to misinterpretation of results.

  • Critical Test Selection: Selecting the right hypothesis test is pivotal. Whether it’s a parametric test like t-tests or ANOVA for normally distributed data, or non-parametric tests like Mann-Whitney U or Kruskal-Wallis for non-normally distributed data, making the correct choice ensures the reliability and validity of results.

  • Meaningful Results: Correctly executed hypothesis testing yields meaningful results that can drive scientific discoveries, support evidence-based management practices, and contribute to the conservation of ecological systems.

  • Interdisciplinary Application: The principles of hypothesis testing transcend disciplinary boundaries. Researchers in forestry and ecology can benefit from statistical rigor, ensuring that their findings are robust and actionable.

  • Continuous Learning: As statistical methods and tools evolve, researchers should stay current with best practices in hypothesis testing. Ongoing education and collaboration with statisticians or data scientists can enhance the quality of research.

  • Ethical Considerations: Sound hypothesis testing is not only about finding statistical significance; it also carries ethical implications. Responsible interpretation of results and transparent reporting are essential for maintaining scientific integrity.

In summary, hypothesis testing plays a pivotal role in advancing knowledge in forestry and ecology. It empowers researchers to rigorously assess hypotheses, make data-driven decisions, and contribute to the sustainable management of ecosystems and forests. Proper test selection and hypothesis formulation are essential to derive meaningful insights from data, fostering interdisciplinary collaboration and ethical scientific practice.

12.2 Confidence Intervals, p-values Interpretation, and Correlation Test

Unraveling the Mysteries of Statistical Inference

12.2.1 The Significance of Confidence Intervals, p-Values, and Correlation Tests in Forestry and Ecology

  • Informing Decision-Making: These statistical concepts are critical tools that help researchers in forestry and ecology make informed decisions based on empirical evidence. They go beyond raw data and provide a framework for interpreting results.

  • Quantifying Uncertainty: Confidence intervals are invaluable for quantifying uncertainty. In forestry and ecology, where ecosystems are inherently complex, it’s rarely possible to make definitive statements. Confidence intervals provide a range of plausible values, giving researchers and policymakers a clearer understanding of the uncertainty surrounding estimates.

  • Assessing Statistical Significance: p-Values serve as a compass for researchers. They indicate the strength of evidence against the null hypothesis. In ecological studies, knowing whether an effect is statistically significant is essential for evaluating the ecological importance of a phenomenon.

  • Understanding Relationships: Correlation tests, such as Pearson’s correlation coefficient or Spearman’s rank correlation, reveal relationships between variables. These relationships can be crucial in forestry for understanding the impact of environmental factors on tree growth or in ecology for studying predator-prey dynamics.

  • Robust Scientific Inference: In forestry, when determining the effectiveness of a silvicultural practice, researchers must assess not only the magnitude of change but also its statistical significance. Similarly, in ecology, it’s not just about observing patterns but rigorously testing hypotheses about ecological interactions.

  • Supporting Conservation Efforts: In ecology, understanding the correlation between environmental factors and species distribution can guide conservation efforts. For example, knowing the correlation between water quality and amphibian populations can inform wetland management practices.

  • Interpreting Ecological Data: Ecology often deals with complex, noisy data. Confidence intervals and p-values help ecologists distinguish meaningful patterns from random fluctuations. They aid in identifying ecologically relevant relationships amidst the intricacies of ecosystems.

  • Quantifying Ecological Risk: In forestry, researchers may use correlation tests to assess the risk factors associated with forest diseases or pest infestations. This information guides strategies for mitigating ecological risks.

  • Informed Policy and Management: Policymakers and forest managers rely on credible ecological research to make decisions about land use, conservation, and resource management. Confidence intervals, p-values, and correlation tests provide the necessary scientific rigor to underpin these decisions.

  • Cross-Disciplinary Collaboration: Forestry and ecology often intersect with other fields such as climatology, hydrology, and geospatial science. Understanding these statistical concepts facilitates collaboration and the integration of diverse datasets.

  • Ethical Scientific Practice: Transparent reporting of results, including confidence intervals and p-values, is an ethical imperative. It ensures that research in forestry and ecology can be critically evaluated, replicated, and built upon by the scientific community.

In summary, confidence intervals, p-values, and correlation tests are not mere statistical jargon; they are the foundation of robust scientific inference in forestry and ecology. They empower researchers to quantify uncertainty, assess significance, and uncover meaningful ecological relationships. These concepts are essential for informed decision-making, effective conservation efforts, and the responsible management of our natural resources.

12.2.2 Confidence Intervals

Definition and Interpretation: A confidence interval is a statistical construct that provides a range of values within which the true population parameter is likely to lie with a certain level of confidence. In forestry and ecology, this means that when we estimate parameters like the average tree height in a forest or the mean plant biomass in a wetland ecosystem, we can express our uncertainty by providing an interval estimate.

For example, a 95% confidence interval indicates that if we were to take many samples and construct intervals from them, about 95% of those intervals would capture the true parameter. This allows us to make more robust inferences about forest characteristics or ecosystem properties.

Constructing Confidence Intervals: Constructing a confidence interval involves several steps:

  1. Collect Sample Data: Gather data from a representative sample of the population.

  2. Calculate Sample Statistics: Compute sample statistics such as the mean and standard error.

  3. Determine Confidence Level: Choose a confidence level, often set at 95% but can vary.

  4. Calculate Margin of Error: This quantifies the uncertainty and depends on the chosen confidence level.

  5. Formulate the Confidence Interval: Create the interval around the sample statistic using the margin of error.

For instance, if you want to estimate the mean plant biomass in a wetland ecosystem with a 95% confidence interval, you’ll collect data, calculate the sample mean and standard error, use the Z or t-distribution for the chosen confidence level, and formulate the interval.

12.2.3 p-values Interpretation

Explanation and Interpretation: A p-value is a crucial tool for assessing the strength of evidence against the null hypothesis in hypothesis testing. It quantifies the probability of obtaining results as extreme as the observed results, assuming the null hypothesis is true.

In the context of forestry and ecology, a small p-value, typically less than 0.05, indicates strong evidence against the null hypothesis. It suggests that the observed effect or relationship is unlikely to have occurred by random chance. This helps researchers make informed decisions about factors affecting ecological systems, like the impact of pollution on amphibian populations or fire frequency on plant species diversity.

12.2.4 Correlation Test

Definition and Types: Correlation tests measure the strength and direction of relationships between two variables. In forestry and ecology, understanding these relationships is pivotal. Two common correlation tests are:

  • Pearson Correlation Coefficient: It assesses linear relationships between variables. For instance, it can be used to examine how temperature affects the number of bird species in a region.

  • Spearman Rank Correlation: This test is suitable for detecting non-linear relationships. In ecological studies, where relationships might not always be linear, Spearman’s rank correlation is invaluable.

Interpreting Correlation Coefficients: Interpreting correlation coefficients is vital for understanding ecological relationships:

  • Positive Correlation: When one variable increases, the other tends to increase. In the context of forestry, this might mean that as tree density increases, so does wildlife diversity.

  • Negative Correlation: When one variable increases, the other tends to decrease. For instance, as pollution levels rise, amphibian populations may decline.

  • Zero Correlation: If the correlation coefficient is close to zero, there’s no linear relationship between the variables. This could signify that changes in one variable do not predict changes in the other.

In summary, these statistical concepts - confidence intervals, p-values, and correlation tests - are indispensable in forestry and ecology. They facilitate rigorous hypothesis testing, quantify uncertainty, and reveal ecological relationships, enabling researchers to make informed decisions about conservation, management, and environmental impact assessments.

12.2.5 Practical Example

  • Research Question: Is there a significant correlation between tree density and the above-ground tree carbon content in the plantations?

    Steps:

    1. Data Collection: In your study, you gather data on tree density (measured in square meters per hectare) and the above-ground tree carbon content measured in various plantation sites.

    2. Data Entry: You enter this data into a spreadsheet or data file. Here’s a simplified example of what your dataset might look like:

      Plantation_age Aboveground_Tree_Carbon_ton_per_ha Tree_Density_per_ha
      7 0.8515 1175
      7 0.7578 1000
      7 0.7726 1275
      7 0.4374 975
      7 0.5888 1275
      7 0.6660 1150
      7 0.6926 1350
      7 0.3777 1125
      7 0.7865 1250
      7 1.2254 1350
      8 0.3627 675
      8 0.2991 775
      8 0.3295 675
      8 0.1241 550
      8 0.4288 600

      R Code Explanation:

      library(haven): In this line, the library() function is used to load the ‘haven’ package. The ‘haven’ package is used for importing and working with data stored in other statistical software formats like SPSS, SAS, and Stata within the R environment. It provides functions to read and manipulate data from these formats.

      library(knitr): This line loads the ‘knitr’ package. ‘knitr’ is a versatile package used for dynamic report generation and literate programming in R. It allows you to create documents that combine R code, results, and narrative text. This is particularly useful for generating reports, papers, or documents that include live R code and its output.

      library(magrittr): Here, the ‘magrittr’ package is loaded. ‘magrittr’ provides a pipe operator (%>%) that simplifies the process of applying a sequence of data manipulation operations to a dataset. It allows you to write code in a more readable and intuitive “pipeline” fashion, making complex operations easier to understand.

      These three lines of code load the specified R packages, making their functions and features available for use in the R script or R Markdown document. This is a common practice at the beginning of an R script to ensure that the required packages are available for use throughout the script.

    3. Performing a Correlation Test: You then conduct a correlation test to evaluate whether there’s a significant relationship between canopy density and the number of bird species. Depending on the distribution of your data, you can choose between the Pearson correlation test for linear relationships or the Spearman rank correlation for non-linear relationships. Here’s how you can perform it using R:

      # Perform a Pearson correlation test
correlation_result <- forest_data %>% 
rstatix::cor_test(
  vars = "Tree_Density_per_ha",
  vars2 = "Aboveground_Tree_Carbon_ton_per_ha",
  alternative = "two.sided",
  method = "pearson",
  conf.level = 0.95,
  use = "pairwise.complete.obs"
)

# Alternatively, you can perform a Spearman correlation test for non-linear relationships:
#correlation_result <- forest_data %>% 
# rstatix::cor_test(
#   vars = "Tree_Density_per_ha",
#   vars2 = "Aboveground_Tree_Carbon_ton_per_ha",
#   alternative = "two.sided",
#   method = "spearman",
#   conf.level = 0.95,
#   use = "pairwise.complete.obs"
# )

# Print the correlation result
print(correlation_result)
      ## # A tibble: 1 × 8
##   var1                var2        cor statistic      p conf.low conf.high method
##   <chr>               <chr>     <dbl>     <dbl>  <dbl>    <dbl>     <dbl> <chr> 
## 1 Tree_Density_per_ha Abovegro…   0.2      1.82 0.0718  -0.0182     0.404 Pears…

      R Code Explanations:

      • Load Necessary Packages:

        • library(rstatix): Loads the ‘rstatix’ package, which provides functions for statistical analysis.

        • library(ggplot2): Loads the ‘ggplot2’ package, a popular package for data visualization.

      • Load Your Dataset:

        • forest_data <- haven::read_sav("./data/Filtered.sav"): Reads a dataset from a SPSS file (‘.sav’) located in the “./data” directory and assigns it to the variable ‘forest_data’. The ‘haven’ package is used for reading SPSS files.

      • Perform a Pearson Correlation Test:

        • correlation_result <- forest_data %>% rstatix::cor_test(...): Calculates a Pearson correlation test between two variables from the ‘forest_data’ dataset.

        • vars = "Tree_Density_per_ha": Specifies the first variable for correlation.

        • vars2 = "Aboveground_Tree_Carbon_ton_per_ha": Specifies the second variable for correlation.

        • alternative = "two.sided": Specifies a two-tailed test to check for correlation in both directions (positive and negative).

        • method = "pearson": Specifies the Pearson correlation method.

        • conf.level = 0.95: Sets the confidence level for the test to 95%.

        • use = "pairwise.complete.obs": Handles missing values by using pairwise complete observations.

      • Print the Correlation Result:

        • print(correlation_result): Prints the correlation result.

    4. The correlation_result will contain valuable information, including the correlation coefficient (often denoted as ‘r’) and the p-value. These statistics are crucial for assessing the strength and significance of the relationship between canopy density and the number of bird species in your forest dataset.

      Remember that interpreting the results is essential. Look at the correlation coefficient (‘r’) to understand the direction and strength of the relationship. A positive ‘r’ indicates a positive linear relationship, while a negative ‘r’ indicates a negative linear relationship. Additionally, pay attention to the p-value; a small p-value (< 0.05) suggests statistical significance, indicating that the observed correlation is unlikely to have occurred by chance.

      Correlation result explanation

      • var1 and var2: These columns specify the variables that were used in the correlation test. In this case:

        • var1 is “Tree_Density_per_ha,” representing one of the variables used in the test.

        • var2 is “Aboveground_Tree_Carbon_ton_per_ha,” representing the other variable used in the test.

      • cor: This column shows the Pearson correlation coefficient (r) between the two variables. In this case, the correlation coefficient is approximately 0.2.

      • statistic: This column displays the test statistic associated with the correlation test. For Pearson correlation, this is often calculated as (correlation coefficient * sqrt((n-2) / (1 - r^2))), where ‘n’ is the sample size. In this case, the test statistic is approximately 1.82.

      • p: The ‘p-value’ (probability value) is shown in this column. It represents the probability of obtaining a correlation as extreme as the observed correlation coefficient (0.2) by random chance, assuming there is no real correlation between the variables. In this case, the p-value is approximately 0.0718.

      • conf.low and conf.high: These columns indicate the lower and upper bounds of the confidence interval for the correlation coefficient. The confidence interval provides a range within which the true population correlation coefficient is likely to fall with a certain level of confidence. In this case, the lower bound is approximately -0.0182, and the upper bound is approximately 0.404.

      • method: This column specifies the method used for the correlation test. In this case, it’s “Pearson,” indicating that a Pearson correlation test was performed.

    5. Interpretation:

      • The Pearson correlation coefficient (r) of approximately 0.2 suggests a weak positive correlation between the variables “Tree_Density_per_ha” and “Aboveground_Tree_Carbon_ton_per_ha.” This indicates that as one variable increases, the other tends to increase, but the relationship is not very strong.

      • The p-value of approximately 0.0718 is greater than the commonly used significance level of 0.05 (5%). This suggests that there is not strong evidence to reject the null hypothesis, which implies that there may not be a statistically significant correlation between the two variables. However, it’s worth noting that the p-value is relatively close to 0.05, so the relationship may still be of interest and should be interpreted cautiously.

      • The confidence interval for the correlation coefficient spans from approximately -0.0182 to 0.404. Since this interval contains zero (0), it further suggests that the correlation is not statistically significant, as it includes the possibility of no correlation (r = 0).

      The results indicate a weak positive correlation between the two variables, but it’s not statistically significant at the conventional significance level of 0.05. Researchers would typically interpret this as there being insufficient evidence to conclude that a significant correlation exists between “Tree_Density_per_ha” and “Aboveground_Tree_Carbon_ton_per_ha” in the studied population. However, further investigation or a larger sample size may be needed to draw more definitive conclusions.

    6. Interpreting the Results: The correlation test provides a correlation coefficient, often denoted as ‘r.’ This coefficient quantifies the strength and direction of the relationship. In our case, if ‘r’ is positive and close to 1, it indicates a positive linear relationship, implying that as tree density increases, the above-ground tree carbon content tends to increase. If ‘r’ is negative and close to -1, it suggests a negative linear relationship. If ‘r’ is close to 0, it indicates a weak or no linear relationship.

      Additionally, the result will typically include a p-value. A small p-value (typically < 0.05) suggests that the observed correlation is statistically significant.

      Your interpretation might be: “There is a statistically significant positive (or negative) correlation (correlation coefficient ‘r’) between tree density and above-ground tree carbon content at a significance level of 0.05.”

      This practical example illustrates how correlation tests are applied in forestry and ecology to assess relationships between ecological variables, providing valuable insights for conservation and management decisions.

12.2.6 Summary

  • Confidence Intervals:

    • Definition: Confidence intervals are statistical intervals that provide a range within which the true population parameter is likely to fall.

    • Importance: They allow us to estimate the precision of sample statistics and infer characteristics of the larger population.

    • Interpretation: For example, a 95% confidence interval means that if we were to repeatedly collect samples and construct intervals, we would expect about 95% of those intervals to contain the true parameter.

    • Practical Use: In forestry and ecology, confidence intervals might be used to estimate the average tree height in a forest, with the interval indicating the plausible range for the true average height.

  • p-values:

    • Explanation: p-values are statistical measures representing the probability of obtaining results as extreme as the observed results, assuming the null hypothesis is true.

    • Significance Level: A common significance level is set at 0.05, meaning there’s a 5% chance of rejecting the null hypothesis when it’s true.

    • Interpretation: A small p-value (< 0.05) suggests strong evidence against the null hypothesis, indicating that the observed results are unlikely to have occurred by chance.

    • Practical Use: In ecological studies, researchers might use p-values to determine whether pollution significantly impacts amphibian populations based on observed data.

  • Correlation Tests:

    • Definition: Correlation tests measure the strength and direction of a linear relationship between two variables.

    • Types: Two common correlation tests are Pearson correlation (for linear relationships) and Spearman rank correlation (for non-linear relationships).

    • Interpretation: Positive correlation indicates that as one variable increases, the other tends to increase; negative correlation means that as one variable increases, the other tends to decrease. Zero correlation means there’s no linear relationship between variables.

    • Practical Use: Ecologists might use correlation tests to assess if there’s a significant relationship between tree canopy density and the number of bird species in a particular forest. A positive correlation would suggest that as canopy density increases, so does the number of bird species.

Confidence intervals provide a way to estimate population parameters, p-values help assess evidence against the null hypothesis, and correlation tests quantify relationships between variables. These tools are fundamental for researchers in forestry and ecology to draw meaningful conclusions from data and make informed decisions.

12.3 Advanced R and Jamovi Data Analysis: T-test, ANOVA, and Linear Regression

Unlocking the Power of t-test, ANOVA, and Linear Regression

12.3.1 Significance of Advanced Data Analysis in Forestry and Ecology Research

Forestry and ecology research often deals with intricate ecosystems, diverse species interactions, and complex environmental factors. To gain deeper insights and make informed decisions in these fields, advanced data analysis plays a pivotal role. Here are some key aspects highlighting its significance:

  1. Uncovering Complex Relationships: Ecological systems are rarely straightforward. Advanced data analysis techniques, such as multivariate analysis or machine learning algorithms, enable researchers to delve deep into complex relationships between various ecological variables. This can reveal hidden patterns and interactions that might not be evident with basic statistical methods.

  2. Environmental Modeling: Forestry and ecology researchers frequently need to model and predict environmental changes, species distributions, or ecosystem responses to disturbances. Advanced analysis tools allow for the development of sophisticated models that incorporate multiple variables, spatial data, and temporal dynamics.

  3. Optimizing Conservation Efforts: In conservation biology, it’s crucial to optimize limited resources to protect endangered species and preserve biodiversity. Advanced analyses can aid in identifying priority areas for conservation, assessing the impact of habitat fragmentation, and designing effective conservation strategies.

  4. Evaluating Climate Change Effects: With climate change impacting ecosystems worldwide, it’s vital to understand how these changes affect plant and animal species. Advanced statistical methods help in assessing climate change impacts, such as shifts in species distribution ranges, phenological changes, or altered migration patterns.

  5. Big Data Challenges: In today’s era of big data, forestry and ecology research often involve vast datasets collected from remote sensors, satellite imagery, or citizen science projects. Advanced data analysis tools provide the means to efficiently handle, process, and extract meaningful information from large and diverse datasets.

  6. Decision Support Systems: Advanced data analysis can be integrated into decision support systems that assist policymakers and land managers in making well-informed choices regarding land use, forest management, or conservation priorities.

  7. Interdisciplinary Research: Forestry and ecology increasingly intersect with other disciplines such as remote sensing, geospatial analysis, and machine learning. Advanced data analysis facilitates interdisciplinary collaboration, enabling researchers to combine expertise and tackle complex environmental challenges.

Advanced data analysis techniques empower forestry and ecology researchers to navigate the intricacies of natural systems, make data-driven decisions, and contribute to our understanding of the complex relationships between ecosystems and the environment. These techniques are essential tools for addressing contemporary ecological and environmental challenges.

12.3.2 t-test

Review of the T-Test:

The t-test is a statistical tool used to determine whether there is a significant difference between the means of two groups. It’s particularly valuable when comparing two groups to assess if the observed differences are likely due to real variation or mere chance.

Example: Comparing the Mean Species Diversity in Two Different Wetland Ecosystems:

Suppose you’re studying two wetland ecosystems, one impacted by human activities and the other left undisturbed. You can use a t-test to determine if there’s a statistically significant difference in species diversity between these two ecosystems.

Types of t-tests

Explanation of Two Types of T-Tests:

There are two primary types of t-tests:

  1. Independent Samples t-test: This test compares the means of two independent groups. It’s suitable when you have two separate groups, and you want to assess if there’s a significant difference between their means.

    Example: Choosing the Appropriate t-test to Compare Soil Nutrient Levels Before and After Fertilization:

    If you want to determine whether fertilization significantly impacts soil nutrient levels, you might collect soil samples before and after applying fertilizers. An independent samples t-test can be used to evaluate if there’s a significant difference in soil nutrient levels between the two independent time points.

  2. Paired Samples t-test: This test compares means within the same group under different conditions. It’s appropriate when you’re working with paired data points, such as before-and-after measurements on the same subjects.

    Example: Choosing the Appropriate t-test to Compare Soil Nutrient Levels Before and After Fertilization (Continued):

    In this case, if you’re collecting soil samples from the same locations before and after fertilization, a paired samples t-test would be suitable to assess if there’s a significant difference in soil nutrient levels due to the treatment.

12.3.3 ANOVA

ANOVA is a statistical technique used to assess whether there’s a significant difference in means among three or more groups. Instead of comparing just two groups like the t-test, ANOVA allows you to evaluate multiple groups simultaneously.

Example: Analyzing the Impact of Three Different Fire Frequencies on Plant Species Richness in Grasslands:

Imagine you’re studying the effects of fire on plant species richness in grasslands, and you have three different fire frequency treatments. ANOVA can help you determine if there’s a significant difference in plant species richness among these three treatments.

12.3.3.1 One-Way ANOVA

One-way ANOVA is a specific type of ANOVA that tests for differences in means among three or more groups. It’s useful when you have a single independent variable with multiple levels or groups.

Example: Evaluating If There’s a Significant Difference in Tree Growth Across Multiple Forest Types:

Suppose you’re studying tree growth across various forest types, such as coniferous, deciduous, and mixed forests. One-way ANOVA can assess if there’s a significant difference in tree growth among these different forest types.

12.3.3.2 Two-Way ANOVA

Two-way ANOVA extends the concept of ANOVA by exploring the influence of two independent categorical variables on a dependent variable. It allows you to examine how these two factors interact and affect the outcome.

Example: Investigating the Interactive Effects of Temperature and Precipitation on Plant Growth:

In ecological research, you might want to understand how both temperature and precipitation levels impact plant growth. Two-way ANOVA enables you to assess whether there are significant main effects of temperature and precipitation and whether there’s an interaction between these two factors affecting plant growth.

12.3.4 Linear Regression

Linear regression is a statistical technique used to assess the relationship between a dependent variable and one or more independent variables. It’s particularly valuable for modeling and predicting how changes in independent variables affect the dependent variable.

Example: Analyzing the Relationship Between Temperature and Butterfly Population Size:

Suppose you’re interested in understanding how temperature influences the population size of a particular butterfly species. Linear regression allows you to quantify this relationship and make predictions about butterfly populations based on temperature variations.

12.3.4.1 Multiple Linear Regression

Multiple linear regression expands upon simple linear regression by considering the influence of multiple independent variables on a single dependent variable. It’s a versatile tool for modeling complex relationships when several factors may affect the outcome.

Example: Predicting Tree Biomass Based on Factors Like Soil Quality, Precipitation, and Sunlight:

In forestry and ecology, you might want to predict tree biomass, which could depend on various factors like soil quality, precipitation, and sunlight. Multiple linear regression enables you to build a comprehensive model that accounts for the combined influence of these multiple independent variables on tree biomass.

These advanced statistical techniques are indispensable in forestry and ecology research for uncovering relationships, making predictions, and drawing meaningful conclusions from complex ecological data.

12.3.5 Practical Example

  • Research Question: Does soil pH, temperature, and precipitation collectively influence plant growth?

    1. Data Collection: To answer this research question, you would collect data on various factors, including soil pH, temperature, precipitation, and plant growth. You might measure soil pH at different locations, record temperature values over time, and track precipitation levels. Simultaneously, you’d measure plant growth, which could be in terms of height, biomass, or other relevant metrics. Each data point represents a combination of these variables.

    2. Multiple Linear Regression Analysis: With your dataset in hand, you’d perform a multiple linear regression analysis. This advanced statistical technique allows you to assess how these multiple independent variables (soil pH, temperature, and precipitation) collectively influence the dependent variable (plant growth). In the regression model, you’ll examine how changes in each independent variable relate to changes in plant growth while controlling for the others.

      • Performing the Analysis: You can use statistical software like R or Jamovi to conduct the multiple linear regression analysis. In R, you’d use functions like lm() to specify the model and estimate coefficients.

      • Model Output: The output of this analysis includes coefficients for each independent variable (soil pH, temperature, and precipitation). These coefficients represent the strength and direction of their respective effects on plant growth. Additionally, you’ll get statistics such as R-squared (which measures the goodness of fit) and p-values (to determine the significance of each predictor).

    3. Interpretation: Upon obtaining the results, you’d interpret them to identify the significant predictors of plant growth. You might find that soil pH and precipitation have significant positive effects on plant growth, while temperature has a negligible effect. The R-squared value would indicate how well the model explains the variance in plant growth based on these predictors.

      • For example, if the regression analysis reveals that a one-unit increase in soil pH leads to a significant increase in plant growth (positive coefficient) and that this relationship is statistically significant (low p-value), you can conclude that soil pH plays a crucial role in influencing plant growth.

    In this practical example, multiple linear regression empowers you to explore how a combination of ecological factors collectively shapes plant growth. It helps you uncover complex relationships and provides insights into which variables have the most substantial impact on plant growth in your specific ecological context.

12.3.6 Summary

In the realm of ecological and environmental research, statistical analysis plays a pivotal role in extracting meaningful insights from complex datasets. Advanced statistical techniques like T-tests, ANOVA, and linear regression offer powerful tools for exploring and understanding ecological phenomena. Here’s a more in-depth look at these key takeaways:

  1. T-Tests, ANOVA, and Linear Regression: These statistical methods are essential tools in the ecologist’s toolkit. They enable researchers to investigate relationships, differences, and patterns within ecological data, helping to address critical research questions.

  2. Choosing the Appropriate Test: The choice of which statistical test to employ should be driven by the nature of the research question and the characteristics of the data at hand. Understanding the nuances and assumptions of each method is crucial in selecting the most suitable approach.

    • For instance, if you aim to compare the means of two groups, a T-test is a relevant choice. If your research involves more than two groups, ANOVA can help assess mean differences. When exploring the relationship between one or more independent variables and a dependent variable, linear regression provides valuable insights.

  3. Data-Driven Insights: Advanced statistical analyses are not just computational exercises; they are pathways to uncovering ecological insights. By conducting these analyses, researchers gain a deeper understanding of ecological systems, allowing them to draw scientifically valid conclusions and make informed decisions.

    • For example, ANOVA may reveal significant differences in plant species richness across different forest types, helping conservationists make informed choices about ecosystem management. Similarly, linear regression can quantify the impact of environmental variables on wildlife populations.

t-tests, ANOVA, and linear regression are invaluable tools that empower ecologists to explore, analyze, and understand ecological data. By selecting the appropriate method and conducting rigorous analyses, researchers can unlock insights that contribute to conservation efforts, environmental policies, and a deeper comprehension of the natural world.